Colloquium

Speaker: Taylor Brysiewicz (Notre Dame)

"Computational Enumerative Geometry - Theory and Applications"

Time: 14:30

Room: Zoom

Many theoretical and applied problems may be viewed through the lens of enumerative geometry: the area of algebraic geometry concerned with counting geometric objects which satisfy prescribed conditions. Computational enumerative geometry uses computers to study such problems. In this talk, I will showcase instances where numerical algebraic geometry, symbolic algebra, and combinatorics came together to answer questions in various applications, such as optimization, theoretical physics, and mechanism design.

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3:30-4pm Meet and Greet

https://gather.town/app/QpSa5CyNCP4WrNKm/MathTea

Colloquium

Speaker: Yasha Berchenko-Kogan (Pennsylvania State University)

"Geometry and Computation"

Time: 14:30

Room: Via Zoom

Geometric ideas can help us understand and develop computational methods. In turn, numerical methods let us compute and visualize geometric objects. I will illustrate the fruitful interaction between these two fields with examples from mathematical neuroscience, numerical analysis, and mean curvature flow.

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https://westernuniversity.zoom.us/j/95109938102

Meeting ID: 951 0993 8102

Passcode: talks

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Analysis Learning Seminar

Speaker: Rasul Shafikov (Western)

"Foliations, Poincare metric, Uniformazation"

Time: 15:40

Room: MC 108

This is the first talk in the series with the goal of understanding recent results due to M. Brunella concerning Poincare metric on algebraic surfaces equipped with a singular holomorphic foliation.

Colloquium

Speaker: David White (Denison University)

"The Kervaire Invariant One Problem and the Blumberg-Hill Conjecture"

Time: 14:00

Room: Zoom

In a 2016 Annals paper, Hill, Hopkins, and Ravenel solved the Kervaire Invariant One Problem using tools from equivariant stable homotopy theory. This problem goes back over 60 years, to the days of Milnor and the discovery of exotic smooth structures on spheres. Of particular importance it its solution were equivariant commutative ring spectra and their multiplicative norms. A more thorough investigation of multiplicative norms, using the language of operads, was recently conducted by Blumberg and Hill, though the existence in general of their new “N-infinity” operads was left as a conjecture. In this talk, I will provide an overview of the Kervaire problem and its solution, I will explain where the operads enter the story, and I will prove the Blumberg-Hill conjecture using a new model structure on the category of equivariant operads.

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https://westernuniversity.zoom.us/j/95109938102

Meeting ID: 951 0993 8102

Passcode: talks

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Algebra Seminar

Speaker: Juan Esteban Rodriguez Camargo (postponed to 3/4/22) (ENS de Lyon)

"Solid locally analytic representations of p-adic Lie groups"

Time: 14:30

Room: ZOOM

In this joint work with Joaquin Rodrigues Jacinto, we develop the theory of locally analytic representations from the perspective of Condensed mathematics of Clausen-Scholze. Taking as inspiration foundational works on the subject from Lazard/Schneider - Tetelbaum/Emerton, etc., we reprove and generalize some cohomological comparisons between continuous, locally analytic and Lie algebra cohomology.

Colloquium

Speaker: Luis Scoccola (Northeastern)

"Data analysis and multiparameter persistence"

Time: 14:30

Room: MC 108

Algorithms in data science often take parameters, which are chosen using rules of thumb or by making strong assumptions about the data. Persistence theory studies parametrized families of topological spaces by means of algebraic objects called persistence modules and, by describing the structure of persistence modules, it provides us with topological descriptors that summarize the varying topology of a parametrized family of spaces. In particular, persistence can be used to summarize the output of many geometric algorithms as we vary their parameters, and thus provides novel tools for parameter selection. It was recognized early in the development of persistence that the structure of persistence modules with two or more parameters -- called multiparameter persistence modules -- is significantly more complicated than the structure of their one-parameter counterparts and much effort has gone into the development of descriptors for multiparameter persistence modules. I will describe two related research programs of mine: applications of multiparameter persistence to density-based clustering, and the development of visualizable and stable descriptors of multiparameter persistence modules using tools from relative homological algebra.

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https://westernuniversity.zoom.us/j/95109938102

Meeting ID: 951 0993 8102

Passcode: talks

One tap mobile

+16475580588,,95109938102#,,,,*776449# Canada

https://gather.town/app/QpSa5CyNCP4WrNKm/MathTea

Analysis Learning Seminar

Speaker: Rasul Shafikov (Western)

"Line bundles and sheaf cohomology"

Time: 11:30

Room: MC 106

We will review the basics of vector bundles, sheafs, and sheaf cohomology

Colloquium

Speaker: Susanna Spektor (Sheridan College)

"Journey into Big Data Science"

Time: 14:30

Room: Zoom

Nowadays the Big Data is all around us, and it is important to understand the tools and mechanisms on collecting and analysing it.

I will start my talk by reviewing real-life problems which scientists are facing when working with a Big Data. Then, I will continue discussing on how those problems can be solved using Wavelet Analysis, Graph Theory, Random Matrices, Probability and Statistics. In this part, I will present some of my past and ongoing research works in these areas of mathematics. Also, I will talk about applications of Big Data in Compressed Sensing, Wireless Communication and Speech Recognition.

The conclusion of the talk will be based on discussion of my future research questions concerning different applied problems of Big Data in the areas of Network Engineering, Financial Mathematics and Bio-Sciences, and their solutions with the help of different areas of mathematics.

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https://westernuniversity.zoom.us/j/95109938102

Meeting ID: 951 0993 8102

Passcode: talks

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Algebra Seminar

Speaker: Oussama Hamza (Western)

"Isotypical components and Zassenhaus filtration"

Time: 14:30

Room: ZOOM

During the 1960s, Jennings, Golod, Shafarevich and Lazard introduced two sequences of integers a and c, closely related to a special filtration of a finitely generated pro-p group G, called Zassenhaus filtration. These sequences give the cardinality of G, and characterize its topology. Let us cite the famous Gocha's alternative: this is a condition on a and c equivalent for G to be analytic, i.e., a Lie group over p-adic fields. Recently in 2016, Minac, Rogelstad and Tan inferred an explicit relation between a and c.This talk will review these results, enrich them in an isotypical context, and give examples.

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https://westernuniversity.zoom.us/j/96866090477

Analysis Learning Seminar

Speaker: Rasul Shafikov (Western)

"Line bundles and divisors"

Time: 11:30

Room: MC 107

We will review the basics of line bundles, divisors, and connection between them.

Algebra Seminar

Speaker: Reading Week - no seminar (Western)

"no seminar"

Time: 14:30

Room: MC 108

Random Matrix Theory Seminar

Speaker: Nathan Pagliaroli (Western)

"Exploring Free Probability I"

Time: 14:40

Room: MC 106

The field of Free Probability was first started in the 1980’s by Dan-Virgil Voiculescu. He was investigating a property called freeness in the context of operator algebras. Eventually these ideas developed in a way to study non-commutative probability spaces. This later lead to connections with random matrices. Properties and concepts in Free Probability often have direct analogues with those in classical probability. We will begin with developing the notation of free independence which corresponds to independence in classical probability theory.

Geometry and Combinatorics

Speaker: Dan Bath (KU Leuven)

"Logarithmic Comparison Theorems for Hyperplane Arrangements, Twisted or Otherwise"

Time: 15:30

Room: Zoom

In the 1990s, Terao and Yuzvinsky conjectured that reduced hyperplane arrangements satisfy the Logarithmic Comparison Theorem, asserting that the logarithmic de Rham complex computes the cohomology of the arrangement's complement. Essentially, this replaces the Brieskorn algebra in Brieskorn's Theorem with the logarithmic de Rham complex. We prove this conjecture by, among other things, sharply bounding the Castelnuovo--Mumford regularity of logarithmic j-forms of a central, essential, reduced arrangement. Time permitting we will discuss how to extend this untwisted Logarithmic Comparison Theorem to a twisted version. Here the twisted logarithmic de Rham complex computes the cohomology of the arrangement's complement with coefficients the rank one local system corresponding to the twist. Unlike the twisted Orlik--Solomon algebra, which can only computes a subset of the rank one local systems on the complement, this generalization computes all such rank one local systems.

Algebra Seminar

Speaker: Juan Esteban Rodriguez Camargo (ENS de Lyon)

"Solid locally analytic representations of p-adic Lie groups"

Time: 14:30

Room: ZOOM

In this joint work with Joaquin Rodrigues Jacinto, we develop the theory of locally analytic representations from the perspective of Condensed mathematics of Clausen-Scholze. Taking as inspiration foundational works on the subject from Lazard/Schneider - Tetelbaum/Emerton, etc., we reprove and generalize some cohomological comparisons between continuous, locally analytic and Lie algebra cohomology.