This seminar takes place within the scope of the master's course "Seminário em Matemática Pura". This is a public session where a presentation is made by the student.
 
Room 4.6, Building VIII

Abstract:
For germs of plane curves, Zariski proved that an irreducible plane curve germ is analytically equivalent to an irreducible plane curve germ with finite Puiseux parametrization. Germs of plane curve germs represent the simplest instance of quasi-ordinary hypersurfaces in dimension two. Zariski’s algebraic techniques cannot be applied to the general case. We show that, for some types of quasi-ordinary surfaces, these techniques can indeed be applied in the context of contact geometry. This is an ongoing work for my thesis.

Online seminar

Abstract:
Coding theory, originated in the late 1940s, is driven by the need toensure reliable communication over noisy channels. Linearerror-correcting codes, in particular, became central to the fielddue to their algebraic structure and practical utility. These codescan be studied via combinatorial, algebraic, and geometric methods:to each code one associates a matroid from its generator orparity-check matrix, and the independent sets of the matroid define asimplicial complex whose Stanley–Reisner ring captures the code’scombinatorial structure. The Betti numbers of this ring encode keyinvariants of the code. Computing them is difficult in general, butthey reflect important parameters and offer new perspectives on thecode’s structure. In this talk, we will focus on the homologicalinvariants of certain families of BCH codes. BCH codes are regardedas one of the most useful codes in the theory of error-correctingcodes. Despite their prominence, basic properties such as dimensionand minimum distance remain unresolved in many cases. Timepermitting, we will discuss open problems such as Charpin’sconjecture regarding the minimum distance of primitive BCH codes.

Venue: office XX, XX floor of the "Departamento de Engenharia Mecânica e Industrial (DEMI)" Building

Room: 4.6, ed. VIII

Abstract: The concept of a determinant associated with a finite group originates in the work of Dedekind and Frobenius in the late 19\textsuperscript{th} century. This idea was later extended to finite semigroups, where the determinant of the semigroup algebra captures deep structural information. For commutative semigroups, Steinberg provided a factorization of the semigroup determinant, and more recently, the theory has been developed for broader classes, such as semigroups in the pseudovariety $\ensuremath{\mathsf{ECom}}$, where all idempotents commute.

In this talk, we trace the development of computing determinants for finite semigroups, from its classical origins to more recent results. We focus on semigroups whose structure enables determinant computation via partial orders and canonical decompositions, particularly using the notion of $\ll$-smoothness. These developments highlight both the possibilities and limitations in extending the theory beyond commutative and idempotent-commuting settings.

We also discuss recent progress in identifying broader classes of semigroups where determinant computations remain tractable, even when full $\ll$-transitivity is absent. This opens new directions for understanding the algebraic and combinatorial properties that govern the behavior of semigroup determinants.

Venue: office XX, XX floor of the "Departamento de Engenharia Mecânica e Industrial (DEMI)" Building

Venue: office XX, XX floor of the "Departamento de Engenharia Mecânica e Industrial (DEMI)" Building

Venue: office XX, XX floor of the "Departamento de Engenharia Mecânica e Industrial (DEMI)" Building

Statistics and Risk Management Seminar

Department of Mathematics, NOVA MATH/FCT NOVA

Title: Illuminating Distributions: Wavelet-Based Quantile Density Estimation with Applications in Auction Theory

Speaker: Hassan Doosti, Macquarie University's School of Mathematical and Physical Sciences, Sidney, Australia

Date | Time: June 26, 2025 | 14:00

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

Abstract: Quantile density functions, which capture the local structure of probability distributions, have emerged as powerful tools in fields ranging from risk analysis to economic modeling. In this talk, we delve into advanced nonparametric strategies for estimating quantile density functions, spotlighting the versatility and precision of wavelet-based techniques. We investigate a range of estimators—including linear, hard thresholding, and block thresholding approaches—within both unbiased and length-biased sampling frameworks. A key focus is placed on the challenges introduced by sampling bias and the use of adaptive wavelet methods for effective bias correction. Through the lens of auction theory, we demonstrate how quantile-driven insights can unravel bidder behavior and valuation dynamics. Supported by simulation studies and real-world case examples, the presentation underscores the power of wavelet methods in handling complex and irregular data landscapes.

Short Bio: Dr. Hassan Doosti is a Senior Lecturer in Statistics at Macquarie University's School of Mathematical and Physical Sciences. He also serves as the Program Director for the Master of Data Science program. Dr. Doosti specializes in flexible modeling techniques, particularly in nonparametric curve estimation, focusing on scenarios involving incomplete or biased data. His research encompasses areas such as probability density, quantile density, and regression functions. With a prolific publication record exceeding 70 research papers, he has contributed significantly to the field. Dr. Doosti has also edited volumes, including Flexible Nonparametric Curve Estimation and Ethics in Statistics: Opportunities and Challenges. His work bridges theoretical advancements with practical applications across various domains, including medical studies and business analytics.

Organizers: Isabel Natário and Mina Norouzirad

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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)

Venue: office XX, XX floor of the "Departamento de Engenharia Mecânica e Industrial (DEMI)" Building