Title: Nyström methods for Fredholm integral equations defined on planar domains.

Speaker: Maria Grazia Russo (Department of Engineering, University of Basilicata, Italy).

Time: Wednesday, 25 September 2024, from 14:15 to 15:15.

Place: Room1.6, building VII.

Abstract: The talk is devoted to a general Nyström scheme for approximating bivariate linear integral equations of the second kind defined on suitable domains of the plane.
        The basic idea of the numerical strategy is to use a global approach, that is to use cubature rules built starting from a polynomial approximation scheme.
        In fact, the global approximation allows to obtain excellent convergence results, since the order of convergence of the corresponding Nyström methods, is the same as the best polynomial approximation of the solution in suitable selected spaces of functions. Furthermore, in this context it is quite easy to prove the stability of the methods and the good conditioning of the involved linear systems.
        We will give an overview of several results obtained in the last few years, starting from rectangular bounded or unbounded domains, also in the case where the known functions of the equation may have singularities on the boundaries, and arriving at the case of equations defined on curvilinear domains.

Title: Numerical methods for delay and fractional differential equations.

Speaker: Neville J. Ford* (University of Chester, UK).

Date| Time: Wednesday, 16 October 2024, from 14:15 to 16:15 - Room 1.4, building VII.

Abstract: We will consider how to solve delay differential equations and fractional differential equations using numerical schemes. To understand how to do this, we will begin by considering the fundamental theory associated with these equations. We look at the dimension of the underlying dynamical systems to explain how approximation schemes should be set up, and how their performance should be judged. In particular, we shall look at initial and boundary conditions needed to ensure a unique solution and we will see how these must be related to the numerical schemes. If time permits, we shall consider some fractional problems with delays and see how the insights from both types of problems combine in this case.

*https://www.researchgate.net/profile/Neville-Ford

Enhancing the Efficiency and Stability of Deep Neural Network Training through
Controlled Mini-batch Algorithms
The exponential growth of trainable parameters in state-of-the-art deep neural networks
(DNNs), driven by innovations such as self-attention layers and over-parameterization, has led
to the development of models containing billions or even trillions of parameters. As training
datasets grow larger and tasks become more complex, the current challenge lies in balancing
convergence guarantees with the increasing need for efficient training. In this work, we focus on
supervised deep learning, where the training problem is formulated as the unconstrained
minimization of a smooth, potentially non-convex objective function with respect to network
weights.
We propose an approach based on Incremental Gradient (IG) and Random Reshuffling (RR)
algorithms, enhanced with derivative-free extrapolation line-search procedures. Specifically, we
present the Controlled Mini-batch Algorithm (CMA), proposed in [1], which incorporates
sufficient decrease conditions for the objective function and allows for line-search procedures to
ensure convergence, without assuming any further hypotheses on the search direction. We also
present computational results on large-scale regression problems.
We further introduce CMA Light, proposed in [2], an enhanced variant of CMA with
convergence guarantees within the IG framework. Using an approximation of the real objective
function to verify sufficient decrease, CMA Light drastically reduces the number of function
evaluations needed and achieves notable performance gains. We discuss computational results
both against CMA and against state-of-the-art optimizers for neural networks, showing a
significant advantage of CMA Light in large-scale classification tasks using residual
convolutional networks.
Finally, we present the Fast-Controlled Mini-batch Algorithm (F-CMA), extending the
convergence theory of CMA Light to the case where samples are reshuffled at each epoch. We
develop a new line-search procedure, and demonstrate F-CMA's superior performance when
training ultra-deep architectures, such as transformers SwinB and SwinT with up to 130 millions
of trainable parameters. Our results show significant advantages in both stability and
generalization compared to state-of-the-art deep learning optimizers.

Title: Numerical methods for delay and fractional differential equations.

Speaker: Neville J. Ford* (University of Chester, UK).

Date| Time: Friday, 18 October 2024, from 14:15 to 16:15 - Room 3.2, building VII.

Abstract: We will consider how to solve delay differential equations and fractional differential equations using numerical schemes. To understand how to do this, we will begin by considering the fundamental theory associated with these equations. We look at the dimension of the underlying dynamical systems to explain how approximation schemes should be set up, and how their performance should be judged. In particular, we shall look at initial and boundary conditions needed to ensure a unique solution and we will see how these must be related to the numerical schemes. If time permits, we shall consider some fractional problems with delays and see how the insights from both types of problems combine in this case.

*https://www.researchgate.net/profile/Neville-Ford

Title: A mathematical framework for dynamical social interactions with dissimulation.

Speaker: Max O. Souza (Center for Mathematics and Applications (NOVA Math), NOVA FCT, Universidade NOVA de Lisboa, Portugal).

Time: Wednesday, 23 October 2024, from 14:15 to 15:15.

Place: Room 1.6, building VII.

Abstract: Modeling social interactions is a challenging task that requires flexible frameworks. For instance, dissimulation and externalities are relevant features influencing such systems --- elements that are often neglected in popular models. This paper is devoted to investigating general mathematical frameworks for understanding social situations where agents dissimulate, and may be sensitive to exogenous objective information. Our model comprises a population where the participants can be honest, persuasive, or conforming. Firstly, we consider a non-cooperative setting, where we establish existence, uniqueness and some properties of the Nash equilibria of the game. Secondly, we analyze a cooperative setting, identifying optimal strategies within the Pareto front. In both cases, we develop numerical algorithms allowing us to computationally assess the behavior of our models under various settings. Joint work with Y Saporito and Y Thamsten.

Seminar room, building VII
 
 
Abstract:
The rational numbers have been used to measure quantities since ancient times; however, their implementation in computer languages raises a significant problem: zero has no inverse. To address this issue, J. Bergstra and J. Tucker introduced an algebraic structure called a meadow, which allows for the inversion of zero.

In this talk, I will introduce meadows and their various classes, demonstrating that they correspond to labelled lattices, where the rings label the vertices. We will explore how concepts from ring theory, such as Artinian rings and decomposition theorems, can be adapted to this new context. Finally, I will present a connection between meadows and sheaves over a topological space, highlighting the implications of this relationship.

- J. Dias and B. Dinis. "Strolling through common meadows." Communications in Algebra, 2024, 1–28.
- J. Dias and B. Dinis. "Towards an enumeration of finite common meadows." International Journal of Algebra and Computation, 2024, 1-19.
- J. Dias, B. Dinis and P. Marques. Bridging Meadows and Sheaves. arXiv:2410.05921

Zoom link: https://videoconf-colibri.zoom.us/j/91864016501?pwd=J0qrDNWOva0DeM1XTOuUiDN3ToRd3b.1
 
The classical theory of type A crystals provides a graphical framework for proving Schur positivity results. In this talk we will discuss a new category of "square root crystals" (introduced implicitly in work of Yu) that can be used to establish instances of Grothendieck positivity. For example, Buch's combinatorial interpretation of the coefficients expanding products of symmetric Grothendieck functions has a simple description in terms of the tensor product for this category. We will also discuss some shifted analogues and applications to a conjectural formula of Cho-Ikeda for K-theoretic Schur P-functions.

Let F be a finite field and let m, d and r be positive integers. Consider the following
question: What is the maximum number of common zeros over F that a system of r linearly
independent homogeneous polynomials of degree d in m + 1 variables can have?
Because of homogeneity, we will disregard the trivial zero (viz., the origin) and regard two
zeros as equivalent if they are proportional to each other, i.e., if one is obtained from another
upon multiplying all coordinates with a nonzero scalar. In other words, we look for zeros in
the m -dimensional projective space over the field F.
This question was first raised by M. Tsfasman in the case of a single homogeneous
polynomial, i.e., when r = 1. It was then settled by J.-P. Serre (1991). Later Tsfasman
together with M. Boguslavsky formulated a remarkable conjecture in the general case, and
this was shown to hold in the affirmative in the next case of r = 2 by Boguslavsky (1997).
Then about two decades later, it was shown that the conjecture is valid conjecture is valid if
the number of polynomials is at most the number of variables, i.e., r ≤ m + 1, but the
conjecture can be false in general. Newer conjectures were then formulated and although
there has been considerable progress concerning them, the general case is still open.
These questions are intimately related to the study of maximal sections of Veronese varieties
by linear subvarieties of the ambient projective case, and also to the study of the an important
class of linear error correcting codes, called projective Reed-Muller codes.
In this talk, we will outline these developments and explain the above connections.
An attempt will be made to keep the prerequisites at a minimum.

I will give a brief introduction to Algebraic Machine Learning (AML), a purely algebraic method that does not use statistics, search or optimization. Instead, AML relies on semantic embeddings in semilattices and subdirect decompositions. AML is capable of learning from data and also from just a problem statement in the form of a set of formulas; for example, AML can learn to find Hamiltonian Cycles from the problem statement. With the same algorithm, AML can learn from data (e.g. classifying medical images) with a test accuracy that rivals that of deep multilayer perceptrons. I will also give an introduction to Atomized Semilatices, a mathematical method developed to operate and compute AML models.

Abstract: Integrating public transport in sustainable last-mile delivery

We consider a delivery system for last-mile deliveries in urban areas based on the use of Public Transport Service. The idea is to exploit the spare capacity of public transport means to transport parcels within urban areas, thus reducing externalities caused by commercial delivery vans. Specifically, the system is such that parcels are first transported from origins to drop-in stations on public vehicles itineraries. Then, they are transported through public vehicles to drop-out stations, from where they are delivered to destination by freighters using green vehicles. The system is known as Freight-On-Transit (FOT). We present the optimization problem related with and operational decisions, as well as ad-hoc solution methodologies and simulations on synthetic data. 

SHORT BIO

ARCHETTI CLAUDIA

Claudia Archetti is Associate Professor of Operations Research at University of Brescia. From September 2021 to September 2024, she was Full Professor in Operations Research at ESSEC Business School in Paris. The main areas of the scientific activity are: models and algorithms for vehicle routing problems; mixed integer mathematical programming models for the minimization of the sum of inventory and transportation costs in logistic networks; exact and heuristic algorithms for supply-chain management; reoptimization of combinatorial optimization problems. 

She is author of more than 100 papers in international journals. She is co-Editor in Chief of Networks. She was VIP3 of EURO, the Association of European Operational Research Societies, in charge of publications and communication.

Joint with Analysis Seminar

Laboratory 2.2, Building VII

Abstract:
In recent years, the interplay between permutations groups and transformations semigroups has lead to many interesting new results. In particular, the application of the classification of finite simple groups to problems in transformation semigroups paved the way for the exploration of new and interesting ideas, and it led to the production of impressive mathematics involving combinatorics, automata theory, and algebra.

Underlying this connection  is the realization that unit groups profoundly shape the structure of any containing monoids. For example, the endomorphism monoid of a mathematical object is restricted by its isomorphism group. Conversely, important properties of monoids of transformations can often be translated into properties of permutation groups and lead to natural questions about group actions on partitions and sections.

In this seminar, we will look at several cases of transversal properties.

This is joint work with João Araújo (Universidade Nova de Lisboa), João Pedro Araújo (Stanford University), Peter J. Cameron (University of St Andrews), and Pablo Spiga (University of Milano-Bicocca).

Title: Optimization Models for Unit Commitment in Electric EnergySystems

Speaker: Miguel F. Anjos (University of Edinburgh)

Description: The unitcommitment (UC) problem addresses a fundamental decision that is taken whenoperating a power system, namely to set the schedule of power production foreach generating unit in the system so that the demand for electricity is met atminimum cost. The schedule must also ensure that each unit operates within itstechnical limits; these typically include ramping constraints and minimumuptime/downtime constraints. Units that are scheduled to produce electricityduring a given time period are said to be committed for that period. Variousjurisdictions solve UC on a daily basis. In particular, it is the standard toolto clear spot markets, and particularly the day-ahead markets in the USA. InNorth American jurisdictions without markets, the system operators use UC todetermine the day-ahead commitments and dispatches. This mini-course will coversome of the most relevant mathematical optimization models for UC and lead upto open research problems. 

Part I, 27^thNovember, 15:00 – 18:00 - Basics of Unit Commitment and Modern Electric Energy Systems 

Part II, 28^th November, 14:00-17:00 - Unit Commitment Under Uncertainty & Additional Topics

Registrationcan be completed here.

Other info: 

The lectures will be based on the tutorial: 

M.F. Anjos and A.J. Conejo. Unit Commitmentin Electric Energy Systems, Now Foundations and Trends, 2017 (ISBN978-1-68083-370-6). http://dx.doi.org/10.1561/3100000014

Participants should have a laptop computer with access to theinternet. No specific software is required. Knowledge of AMPL or a similar optimizationmodelling language will help but is not essential as the mini-course will beself-contained in this regard. 

Title: Optimization Models for Unit Commitment in Electric EnergySystems

Speaker: Miguel F. Anjos (University of Edinburgh)

Description: The unitcommitment (UC) problem addresses a fundamental decision that is taken whenoperating a power system, namely to set the schedule of power production foreach generating unit in the system so that the demand for electricity is met atminimum cost. The schedule must also ensure that each unit operates within itstechnical limits; these typically include ramping constraints and minimumuptime/downtime constraints. Units that are scheduled to produce electricityduring a given time period are said to be committed for that period. Variousjurisdictions solve UC on a daily basis. In particular, it is the standard toolto clear spot markets, and particularly the day-ahead markets in the USA. InNorth American jurisdictions without markets, the system operators use UC todetermine the day-ahead commitments and dispatches. This mini-course will coversome of the most relevant mathematical optimization models for UC and lead upto open research problems. 

Part I, 27^thNovember, 15:00 – 18:00 - Basics of Unit Commitment and Modern Electric Energy Systems 

Part II,28^th November, 14:00-17:00 - Unit Commitment Under Uncertainty & Additional Topics

Registrationcan be completed here.

Other info: 

The lectures will be based on the tutorial: 

M.F. Anjos and A.J. Conejo. Unit Commitmentin Electric Energy Systems, Now Foundations and Trends, 2017 (ISBN978-1-68083-370-6). http://dx.doi.org/10.1561/3100000014

Participants should have a laptop computer with access to theinternet. No specific software is required. Knowledge of AMPL or a similar optimizationmodelling language will help but is not essential as the mini-course will beself-contained in this regard. 

Room 2.3, building VII

Abstract:
We show that the key map on crystals of any classical type can be reduced to a key map on simply-laced types by using virtualization of crystals. Our proofs are type-free and crystal model independent. The virtualization map also induces an embedding on the Weyl groups by the diagram folding. Thus our results also apply to uniform models like the alcove and the Lakshmibai–Seshadri paths.

As a direct application we obtain new algorithms to compute evacuation, keys, and Demazure atoms in type B_n in terms of Kashiwara–Nakashima tableaux.  In particular, we are able to use type A_n and C_n methods. For type C_n, we apply  results obtained by Azenhas–Tarighat Feller–Torres, Azenhas–Santos and Santos. This is a joint work with González, Huang and Torres.

Title: Pulse vaccination in a SIR model: Global dynamics, bifurcations and seasonality.

Speaker: Alexandre Rodrigues (ISEG - Universidade de Lisboa, Portugal).

Time: Wednesday, 4 December 2024,from 14:15 to 15:15.

Place: Room 1.6, building VII.

Abstract: In this talk, I analyze a periodically forced dynamical system inspired by the SIR model with impulsive vaccination. I characterize its dynamics according to the proportion of vaccinated individuals and the time between doses. I draw the associated bifurcation diagram. I also explore analytically and numerically chaotic dynamics by adding seasonality to the disease transmission rate. This is a joint work with João Maurício de Carvalho (University of Porto).

Zoom link: https://videoconf-colibri.zoom.us/j/97149261405?pwd=dwPsbvzqf72uSGBWpW0Y11AtJXT6Kn.1
 

The plactic monoid is a central object in algebraic combinatorics. Generally represented with Young tableaux, Cain, Gray and Malheiro proved that it has a confluent presentation with column tableaux as generators.
We will look at a left action of the free monoid A^* on this set of generators by Schensted left insertion. This action defines a monoid, called the stylic monoid, which happens to be a non-trivial finite quotient of the plactic monoid. It has a nice presentation by simply quotienting the plactic monoid by the relations x^2=x for all letters x in A. We will look at some interesting properties using a set of representants, the N-tableaux, paired with insertion algorithms.

If time permits, we will conclude with some generalization and analogous quotients called power quotients.

Based on joint work with C. Reutenauer for the stylic monoid, and with F. Hivert, J. Mitchell, M. Tsalakou, and J.-C. Novelli for the power quotients.

Title: Introduction to Dyadic Analysis.

Speaker: George Tephnadze (University of Georgia, Tbilisi, Georgia).

Lecture 1: Tuesday, 10 December 2024, from 10:00 to 12:00.

Lecture 2: Thursday, 12 December 2024, from 10:00 to 12:00.

Lecture 3: Monday, 16 December 2024, from 10:00 to 12:00.

Lecture 4: Wednesday, 18 December 2024, from 10:00 to 12:00.

Place: Room 1.6, building VII.

Abstract: The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.
   Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.
   This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

Lecture 1: We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

Lecture 2: We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

Lecture 3: We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

Lecture 4: We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

   This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

*https://www.ug.edu.ge/en/persons/full/9177

Title: Introduction to Dyadic Analysis.

Speaker: George Tephnadze (University of Georgia, Tbilisi, Georgia).

Lecture 1: Tuesday, 10 December 2024, from 10:00 to 12:00.

Lecture 2: Thursday, 12 December 2024, from 10:00 to 12:00.

Lecture 3: Monday, 16 December 2024, from 10:00 to 12:00.

Lecture 4: Wednesday, 18 December 2024, from 10:00 to 12:00.

Place: Room 1.6, building VII.

Abstract: The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.
   Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.
   This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

Lecture 1: We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

Lecture 2: We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

Lecture 3: We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

Lecture 4: We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

   This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

*https://www.ug.edu.ge/en/persons/full/9177

Title: Introduction to Dyadic Analysis.

Speaker: George Tephnadze (University of Georgia, Tbilisi, Georgia).

Lecture 1: Tuesday, 10 December 2024, from 10:00 to 12:00.

Lecture 2: Thursday, 12 December 2024, from 10:00 to 12:00.

Lecture 3: Monday, 16 December 2024, from 10:00 to 12:00.

Lecture 4: Wednesday, 18 December 2024, from 10:00 to 12:00.

Place: Room 1.6, building VII.

Abstract: The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.
   Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.
   This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

Lecture 1: We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

Lecture 2: We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

Lecture 3: We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

Lecture 4: We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

   This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

*https://www.ug.edu.ge/en/persons/full/9177

Laboratory 2.2, building VII.

Abstract:

Significant efforts have been made to have LLMs prove theorems, but their reasoning power is very limited. Their problem-solving depends on how problems are phrased, struggling with variations from known patterns. They handle "Do X" better than "Don't do X", as they focus on "X" regardless. Their performance drops in long conversations due to attention mechanism limits. Neural networks aren't built for true reasoning. The current belief claims that symbolic AI offers reasoning but is rarely practical. ProverX is symbolic AI Theorem Proving and during this talk I will show how completely wrong is the current belief. 

Title: Introduction to Dyadic Analysis.

Speaker: George Tephnadze (University of Georgia, Tbilisi, Georgia).

Lecture 1: Tuesday, 10 December 2024, from 10:00 to 12:00.

Lecture 2: Thursday, 12 December 2024, from 10:00 to 12:00.

Lecture 3: Monday, 16 December 2024, from 10:00 to 12:00.

Lecture 4: Wednesday, 18 December 2024, from 10:00 to 12:00.

Place: Room 1.6, building VII.

Abstract: The fact that the Walsh system is the group of characters of a compact Abelian group connects dyadic analysis with abstract harmonic analysis. Later on, in 1947 Vilenkin introduced a large class of compact groups (now called Vilenkin groups) and the corresponding characters, which include the dyadic group and the Walsh system as a special case. Pontryagin, Rudin, Hewitt and Ross investigated such problems of harmonic analysis on groups.
   Unlike the classical theory of the Fourier series, which deals with decomposing a function into continuous waves, the Walsh (Vilenkin) functions are rectangular waves. There are many similarities between these theories, but there are also differences. Much of these can be explained by modern abstract harmonic analysis, which studies orthonormal systems from the point of view of the structure of a topological group. This point of view leads naturally to a new domain of considering Fourier Analysis on locally compact Abelian groups and dyadic (Walsh) group provides an important model on which one can verify and illustrate many questions from abstract harmonic analysis.
   This introduction consists of 4 lectures and is aimed at Ph.D. students and researchers without an initial background on the subject.

Lecture 1: We define the Walsh group and functions and equip this group with the topology and Haar measure. Moreover, we investigate the character functions of the Walsh group, and the representation of the Walsh group on the interval [0,1). We also investigate some rearmament of the Walsh system, which is called the Kaczmarz system, and some generalizations, which are called Vilenkin groups and zero-dimensional groups.

Lecture 2: We define and investigate Dirichlet kernels, Lebesgue constants and partial sums with respect to the Walsh system and show that the localization principle holds for the Walsh-Fourier series and it is not true for the Walsh-Kaczmarz Fourier series. We define Lebesgue points and investigate almost everywhere convergence of subsequences of partial sums of the Walsh-Fourier series of integrable functions.

Lecture 3: We define and discuss Walsh-Fejér kernels and means, Walsh-Lebesgue points and investigate approximation properties and almost everywhere convergence of Fejér means in Lebesgue spaces.

Lecture 4: We define and discuss conditional expectation operators, martingales and martingale Hardy spaces. We also state several interesting open problems in this theory.

   This introduction to dyadic analysis is based on the following recent book (where complementary information and several open problems can be found in more general case):

L. E. Persson, G. Tephnadze and F. Weisz, Martingale Hardy Spaces and Summability of one-dimensional Vilenkin-Fourier Series, Birkhäuser/Springer, 2022.

*https://www.ug.edu.ge/en/persons/full/9177

In this talk, we shalldiscuss the construction of infinitely many global-in-time Höldercontinuous analytically weak solutions to stochastic Euler equations inthree-dimensional periodic domain.

The proof is based on astochastic convex integration technique using Beltrami waves asbuilding blocks.

Zoom link: https://videoconf-colibri.zoom.us/j/92565611443?pwd=diOblm3Pu1aC5vYRMoN1BKd0DyktmB.1

Cayley's Theorem states that any finite monoid can be faithfully represented as a semigroup of transformations (self-maps) of a finite set. The minimum size of such a set is the (minimum transformation) degree of the monoid.

We obtain formulae for the degrees of the most well-studied families of finite diagram monoids, including the partition, Brauer, Temperley-Lieb and Motzkin monoids. For example, the partition monoid Pn has degree 1 + ( B(n + 2) - B(n + 1) + B(n) ) / 2 for n ≥ 2, where these are Bell numbers. The proofs involve constructing explicit faithful representations of the minimum degree, many of which can be realised as (partial) actions on projections.

This is joint work with Reinis Cirpons and James Mitchell, both at Univ St Andrews.

A famous result ofDelort (1991) establishes the concentration-

cancellationphenomenon for approximating solutions of 2D Euler equations

with a vortex sheetwhose vorticity maximal function has a log-decay of order

1/2 . On the otherhand, DiPerna and Majda (1987) showed that if the log-

decay assumption isstrictly larger than 1 then the lack of concentration

(and hence energyconservation) holds. Then the so-called DiPerna-Majda

gap problem asks:concentration-cancellation vs. energy conservation in the

remaining log-range(1/2,1]?

In this talk, afterreviewing earlier contributions to the DiPerna-Majda

gap problem, I willpresent a new approach to this question based on sparse-

ness. This is based onjoint projects with Mario Milman and Daniel Spector.

The talk will beself-contained, and no additional prerequisites are needed.

Abstract:

This talk examines the worst-case complexity in continuous optimization, defined as the computational effort required by an algorithm, in the worst-case scenario, to reduce a stationarity measure below a given positive threshold. We begin with an overview of foundational concepts and key results in worst-case complexity. Next, we delve into recent findings on the complexity of directional direct-search methods for nonsmooth unconstrained problems. Moving to the domain of multi-objective optimization, we highlight its distinctive challenges and recent advances. Finally, we present the worst-case complexity of a trust-region algorithm for solving (strongly) convex smooth unconstrained problems.

This talk is anontechnical overview of some topics of spectral theory of Toeplitz operatorson classical Hardy spaces and their abstract generalizations built upon Banachfunction spaces. We pay special attention to Toeplitz operators with continuousand piecewise continuous symbols.

Lab. 2.2, building VII.




Abstract:
 
We begin with a very introductory overview of classical, intuitionistic, and linear logics. Several proof translations exist between classical and intuitionistic logic (negative translations) [1, 2, 3], as well as between intuitionistic and linear logic (Girard translations) [4, 5]. These translations serve various purposes, including transferring properties between systems, simplifying proofs, facilitating the extraction of constructive computational content from proofs, and controlling the use of logical resources.
 
We will show that all these systems can be expressed as extensions of a basic logical system (essentially, intuitionistic linear logic). By establishing a common logical basis, we are able to formalize a unified approach to devising and simplifying such proof translations [6]. This approach clarifies the relationships between different logical systems, and reveals the underlying structure that connects them. Through this simplification process, we obtain the most well-known translations in the literature.
 
This is joint work with Paulo Oliva and Clarence Protin.

References:

[1] A.S. Troelstra, D. van Dalen, Constructivism in mathematics: An introduction. In Studies in Logic and the Foundations of Mathematics, volume 1, 1988.

[2] M. Heine Sørensen, P. Urzyczyn, Lectures on the Curry-Howard Isomorphism, volume 149. Elsevier, 2006.
 
[3] G. Ferreira, P. Oliva, On various negative translations, Electronic Proceedings in Theoretical Computer Science, 47:21-33, 2011.

[4] J.-Y. Girard, Linear logic, Theoretical Computer Science, 50:1–101, 1987.
 
[5] J.-Y. Girard, A tutorial on linear logic. In Substructural Logics, Studies in Logic and Computation 2, pages 327–355. Oxford Science Publications, 1994.
 
[6] G. Ferreira, P. Oliva, C. Protin, On the various translations between classical, intuitionistic and linear logic. (subm.)
https://arxiv.org/abs/2409.02249

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: On Generalized Mean Reverting Processes with Possible Structural Change

Speaker: Yunhong Lyu,Trent University, Peterborough, Canada

Date | Time: February 11, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: In this presentation, we address the inference problem for the drift parameter in a generalized mean-reverting process, which is well-suited for modeling data exhibiting periodic characteristics. Additionally, we examine the case where linear constraints may be imposed on the drift parameters. We introduce three estimators: the unrestricted estimator, the restricted estimator, and the shrinkage estimator, and evaluate their relative efficiency. Furthermore, we explore change-point detection within this framework. Simulation studies validate the effectiveness of the proposed methods, which are subsequently applied to real-world environmental data. The results highlight the significance of accurate inference and timely change detection in environmental processes. Finally, the proposed methodology is expected to enhance the understanding and management of environmental systems.

Short Bio: Yunhong Lyu is an Assistant Professor in the Department of Mathematics & Statistics at Trent University, specializing in statistical modeling and structural change detection. Her research focuses on the inference problems in mean-reverting processes, such as parameter estimation, hypothesis testing and change-point detection, with applications in economics, health, and environmental studies. She holds a PhD from the University of Windsor and has published work on financial modeling, healthcare economics, and education policy. Beyond her research, she enjoys mentoring and teaching both undergraduate and graduate students.

Organizers: Mina Norouzirad & Isabel Natário

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

--------------------------------------------

  Seminar of Operations Research

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Title: A specialized second-order augmented Lagrangian method for mathematical programs with cardinality constraints

Speaker: Mariana da Rosa, UNICAMP, Brasil

Date | Time: February 12, 2025 | 15h00

Place: FCT NOVA, VII-Second Floor, Seminar room

Abstract:

In this talk, a practical and specialized second-order augmented Lagrangian method for solving mathematical programs with cardinality constraints (MPCaC) is presented. The seminar begins with a review of the stationarity conditions for MPCaC and a discussion of some augmented Lagrangian methods proposed in the literature. The presentation then considers a new approach that incorporates a second-order refinement step tailored to the structure of MPCaC. Under reasonable assumptions, the method ensures convergence to second-order stationary points, making it a potential tool for tackling this class of optimization problems.

Seminar of Analysis

Speaker:   Prof. Manil T. Mohan (Department of Mathematics, Indian Institute of Technology Roorkee, India)

Date/time:   02/19/2025 (Wednesday), at 14:15

Location:   Online via Zoom.

Please find the details below:

Link:  https://videoconf-colibri.zoom.us/j/94188507343?pwd=cbH0CTpLYuAxa5haPOm2DcAYKN0DJQ.1

Meeting ID:  941 8850 7343 

Passcode:  229621

Title:   Navier-Stokes equations-The Million Dollar Problem

Abstract:   The Navier-Stokes equations describe the motion of viscous fluids, which can be expressed mathematically in terms of conservation of momentum and conservation of mass for Newtonian fluids. A fundamental problem in analysis is to decide whether smooth, physically reasonable solutions exist for the three-dimensional Navier-Stokes equations (Navier-Stokes existence and uniqueness problem). In May 2000, the Clay Mathematics Institute announced this problem as one of its seven Millennium prize problems in Mathematics. The aim of this talk is to shed lights on this million dollar open problem in Mathematics.

Joint Seminar  Analysis Group & Mathematics for Health and Life Sciences Thematic Line 

 Speaker:   Nico Stollenwerk (Basque Center for Applied Mathematics)

Date/time:   02/26/2025 (Wednesday), at 14:15

Location:  Room 1.16, VII

[15:00 - 15:15 Coffee break ]

Joint Seminar  Analysis Group & Mathematics for Health and Life Sciences Thematic Line 

 Speaker:  Maíra Aguiar (Basque Center for Applied Mathematics & Ikerbasque - Basque Foundation for Science)

Date/time:   02/26/2025 (Wednesday), at 15:15

Location:  Room 1.16, VII

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

~ PhD Program in Mathematics Seminars ~

Titles:
Title 1:  Da Geração de uma Carteira de Mercado Sintética à Escolha de Resseguro: Uma Abordagem Empírica à Criação de um Fundo Sísmico em Portugal
Title 2: Introduction on the role of catastrophe models in measuring flood risks under climate change conditions

Speakers: João Correia & Beatriz Curioso, PDM & NOVA Math

Date | Time: February 26, 2025 | 14h30
Place: FCT NOVA, VII-Second Floor, Seminar room

Abstracts:
Abstract 1:  Um dos principais trabalhos a desenvolver na tese de doutoramento, prende-se com o estudo de estruturas de resseguro para o grupo de ramos de incêndio e outros danos – o mais exposto a catástrofes naturais – na perspetiva nacional. Assim, um dos objetivos iniciais passou pela construção de um simulador capaz de avaliar e comparar performances de diferentes estruturas de resseguro tradicionais, face a cenários de catástrofe. Para tal, relevou-se necessário colmatar a falta de informação disponível, gerando uma carteira de apólices sintética (recorrendo, essencialmente, a leitura de imagens e otimização linear), cujas suas propriedades reflitam a realidade nacional, plasmada em dados públicos. Por fim, incluiu-se uma metodologia de apoio à decisão (SMART e Trident), hierarquizando o valor acrescentado de cada esquema de resseguro com base em critérios e preferências estabelecidas pelo decisor. Como demonstração, é feito um caso de estudo no contexto de avaliação de vários modelos possíveis para a criação de um sistema de proteção contra fenómenos sísmicos para Portugal (Fundo Sísmico).

Abstract 2: In this talk, I will present the initial research made for my PhD thesis: an overview of the flooding phenomenon, focussing on the underlying risks, and a literature review on flood catastrophe models, including the usual procedures when building this type of models for the insurance sector.

Bios:

Bio1: João Correia: Licenciei-me em Matemática Aplicada à Economia e à Gestão pela Universidade do Algarve (2020) e sou mestre em Matemática Atuarial na NOVA FCT (2023), onde dissertei sobre a realidade atual da cobertura do risco sísmico no setor segurador nacional (em colaboração com a Autoridade de Supervisão de Seguros e Fundos de Pensões (ASF)). Após o mestrado ingressei nos quadros da ASF, no Departamento de Análise de Riscos e Solvência, como atuário, com uma das funções principais associada à realização dos estudos quantitativos de suporte à preparação de uma proposta para a criação de um sistema de proteção contra fenómenos sísmicos, incumbida pelo Governo. Atualmente, enquanto aluno de doutoramento, procuro prosseguir a minha especialização no âmbito das ciências atuariais, nomeadamente em resseguro e gestão de risco para catástrofes, em perfeita simbiose com a minha posição profissional.

Bio2: Beatriz Curioso is currently a PhD student in Mathematics with specialisation in Statistics and Risk Management at NOVA FCT. She completed the BSc in Mathematics in 2018, the MSc in Mathematics and Applications with specialisation in Pure Mathematics in 2021, and the MSc in Actuarial Mathematics in 2024, at the same institution. She has over three years of professional experience in the Pension Funds sector and has recently started working as an Actuary in Non-Life Insurance at Fidelidade.

Organizers: Isabel Natário & Mina Norouzirad & Rui Cardoso

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

~ PhD Program in Mathematics Seminars ~

Title: Modeling Mobility Data during COVID-19 in Portugal

Speaker: André Brito, PDM & NOVA Math

Date | Time: March 5, 2025 | 14h30
Place: FCT NOVA, VII-Second Floor, Lab. 2.2

Zoom:  https://videoconf-colibri.zoom.us/j/88333359956

Abstract: The COVID-19 pandemic highlighted the crucial role of statistical modeling in understanding infectious disease dynamics. This study investigates the spatio-temporal dependencies of viral respiratory infections by incorporating non-traditional data sources, particularly human mobility data. Traditional epidemiological models rely on clinical and surveillance data, but integrating mobility patterns provides a deeper understanding of disease spread. Using publicly available Google Community Mobility Reports, this research analyzes population movement across districts in Portugal. We employ statistical modeling to explain mobility including movement stringency and temperature as predictors. The study explores how mobility metrics evolved throughout the pandemic and their predictive value for epidemiological surveillance. This research underscores the importance of dynamic modeling approaches that account for temporal and spatial variations in mobility patterns. The results contribute to improved public health decision-making, providing a framework for leveraging mobility data in future epidemic responses.

Bio: André Martins Brito is a PhD student in Applied Mathematics at NOVA School of Science and Technology, specializing in Statistics and Risk Management. His research focuses on epidemiology and the modeling of mobility-incidence relationships. With a strong academic background, he holds a master’s degree in Applied Mathematics with a specialization in Actuarial Sciences, Statistics, and Operations Research, and a bachelor’s degree in Mathematics Applied to Economics and Management. His research experience includes a scholarship in epidemiology, contributing to a nationwide project on extreme weather event risk assessment in Portugal. Professionally, he has worked as a Data Analyst/Manager at the Bernhard Nocht Institute for Tropical Medicine, where he managed research databases and statistical analyses and worked as an A&H Regional Underwriting Analyst at AIG Europe, applying statistical methods to risk analysis.

Organizers: Isabel Natário & Mina Norouzirad & Rui Cardoso

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Seminar of Analysis

Speaker:  Alina Shalukhina (Department of Mathematics, NOVA FCT, Portugal)

Date/time:  12/03/2025 (Wednesday), from 14:15 to 15:15.

Location:  Room 1.16, Building VII.

Title:  On interpolation of variable Lebesgue spaces over spaces of homogeneous type

Abstract:  We show that the Hardy--Littlewood maximal operator $M$ is bounded on a variable Lebesgue space $L^{p(\cdot)}(X)$, $1<p_-\leq p_+<\infty$, over a space of homogeneous type $X$ if and only if, for every $q\in(1,\infty)$, the exponent $p(\cdot)$ can be represented as

                          $\frac{1}{p(x)}=\frac{\theta}{q}+\frac{1-\theta}{r(x)},      x \in X,$

so that $M$ is bounded on $L^{r(\cdot)}(X)$ for all sufficiently small $\theta>0$. This is an extension of the analogous result by Diening, Karlovych and Shargorodsky from the Euclidean spaces to spaces
of homogeneous type. Results of this kind are applied for transferring properties like
compactness of linear operators from standard Lebesgue spaces to the variable ones.

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

~ PhD Program in Mathematics Seminars ~

Title: Statistical disclosure control and quality evaluation of synthetic data generated by non-parametric methods

Speaker: Vítor Augusto, PDM & NOVA Math

Date | Time: March 12, 2025 | 14h30
Place: FCT NOVA, VII-Second Floor, Lab. 2.2

Abstract: This PhD aims to continue the work in statistical disclosure control by improving the quality of synthetic data generated through non-parametric methods (such as GAN or CART). To achieve this, it will be necessary to extend existing exact inferential procedures for data generated by single imputation to cases of multiple imputation, perform the computational refinement of the degrees of freedom defined in asymptotic inferential procedures for vectors used in their adaptation to matrix inference, and adapt GAN methods for generating partially or completely synthetic data for a sequence of sensitive variables describing a profile. Finally, simulations will be carried out, along with the application to a real database.

Bio:  Vítor Augusto is a PhD student in Mathematics with a specialization in Statistics and Risk Management at NOVA School of Science and Technology. He also completed his Bachelor's degree in Mathematics and his Master's in Mathematics and Applications, specializing in Actuarial Science, Statistics, and Operational Research at the same institution. Professionally, before starting his PhD, he worked as a Maths teacher in elementary and high schools.

Organizers: Isabel Natário & Mina Norouzirad & Rui Cardoso

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Using R Shiny for teaching statistical methods

Speaker: Alexandra Daub, Lars Knieper & Sophie Potts, Georg-August-University, Goettingen, Germany

Date | Time: March 19, 2025 | 14h00

 Zoom: https://videoconf-colibri.zoom.us/j/88333359956

Abstract: Introducing statistical concepts to a heterogeneous student population with diverse backgrounds can be challenging. Visualizations are often used in lectures and associated exercises in order to assist with that. As these are usually done on lecture slides or (digital) notes, they however remain static not exploiting their potential as teaching material. In addition, students often encounter the hindrance of having to implement the method first when wanting to investigate statistical concepts themselves, for which a basic understanding of the methodology and programming knowledge is needed.
In order to provide students with interactive visualizations combined with explanations and further give the opportunity to adjust parameters of a statistical method, we develop webapps for teaching purposes.
Therefore, the R-Shiny framework is employed. It enables to program interactive webapps directly within R while still being flexible enough to incorporate HTML, Javascript and CSS. The apps offer the potential to teach statistical concepts visually and interactively. Further, students get a low-barrier intuition of statistical concepts before programming and applying these themselves.

Short Bio: xx

Organizers: Mina Norouzirad & Isabel Natário

LogosTodos.JPG

This work is funded by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 (https://doi.org/10.54499/UIDB/00297/2020) and UIDP/00297/2020 (https://doi.org/10.54499/UIDP/00297/2020) (Center for Mathematics and Applications)

Recommender Systems (RSs) are pivotal in diverse domains such as e-commerce, music streaming, and social media.

The first part of the seminar presents a comparative analysis of key loss functions in recommender systems: Binary Cross-Entropy (BCE), Categorical Cross-Entropy (CCE), and Bayesian Personalized Ranking (BPR), which distinguish between positive items (interacted by users) and negative items. While previous studies have empirically shown that CCE outperforms BCE and BPR with the full set of negative items, we provide a theoretical explanation by proving that CCE offers the tightest lower bound on ranking metrics like Normalized Discounted Cumulative Gain (NDCG). Given that using the full set of negatives is computationally expensive, we derive bounds for these losses in negative sampling settings, establishing a probabilistic lower bound for NDCG. Our analysis shows that BPR's bound on NDCG is weaker than BCE’s, challenging the common belief that BPR is superior to BCE in recommender system training.

Beyond loss function analysis, we turn our attention to the robustness of Sequential Recommender Systems against data perturbations. Traditional similarity measures, such as Rank-Biased Overlap, prove inadequate for evaluating ranking stability in finite-length sequences. To address this, we introduce Finite Rank-Biased Overlap, a novel similarity measure tailored for practical scenarios. Through empirical analysis of item removal at different positions in temporally ordered sequences, we demonstrate that the impact on recommendation quality is highly position-dependent, with removals at the end of sequences leading to significant performance degradation.

This course provides a comprehensive overview of neural recommender systems, focusing on their foundations, state-of-the-art advancements, and practical challenges. It covers essential deep learning architectures and techniques that power modern recommender systems, exploring their role in personalizing user experiences across various domains such as e-commerce, entertainment, and social media. Key topics include sequence-based models, which capture sequential user behavior, and Transformer-based approaches, which leverage attention mechanisms for better context understanding. The course also delves into graph-based recommendation models, which model relationships between users and items in complex networks. By the end of the course, students will gain a strong understanding of neural recommender systems, their applications, and the challenges of deploying them in real-world settings.

The course is designed for graduate students and researchers with a foundational understanding of machine learning and deep learning. Familiarity with basic neural network architectures (e.g., CNNs, RNNs) is recommended.

The course will appeal to students from related areas such as natural language processing, and computer vision, and optimization, given its focus on domain-specific applications. The emphasis on ethical considerations and explainability will also interest students working on Safe, Explainable, and Trustworthy AI.

This course provides a comprehensive overview of neural recommender systems, focusing on their foundations, state-of-the-art advancements, and practical challenges. It covers essential deep learning architectures and techniques that power modern recommender systems, exploring their role in personalizing user experiences across various domains such as e-commerce, entertainment, and social media. Key topics include sequence-based models, which capture sequential user behavior, and Transformer-based approaches, which leverage attention mechanisms for better context understanding. The course also delves into graph-based recommendation models, which model relationships between users and items in complex networks. By the end of the course, students will gain a strong understanding of neural recommender systems, their applications, and the challenges of deploying them in real-world settings.

The course is designed for graduate students and researchers with a foundational understanding of machine learning and deep learning. Familiarity with basic neural network architectures (e.g., CNNs, RNNs) is recommended.

Yes, the course will appeal to students from related areas such as natural language processing, and computer vision, and optimization, given its focus on domain-specific applications. The emphasis on ethical considerations and explainability will also interest students working on Safe, Explainable, and Trustworthy AI.

This course provides a comprehensive overview of neural recommender systems, focusing on their foundations, state-of-the-art advancements, and practical challenges. It covers essential deep learning architectures and techniques that power modern recommender systems, exploring their role in personalizing user experiences across various domains such as e-commerce, entertainment, and social media. Key topics include sequence-based models, which capture sequential user behavior, and Transformer-based approaches, which leverage attention mechanisms for better context understanding. The course also delves into graph-based recommendation models, which model relationships between users and items in complex networks. By the end of the course, students will gain a strong understanding of neural recommender systems, their applications, and the challenges of deploying them in real-world settings.

The course is designed for graduate students and researchers with a foundational understanding of machine learning and deep learning. Familiarity with basic neural network architectures (e.g., CNNs, RNNs) is recommended.

Yes, the course will appeal to students from related areas such as natural language processing, and computer vision, and optimization, given its focus on domain-specific applications. The emphasis on ethical considerations and explainability will also interest students working on Safe, Explainable, and Trustworthy AI.