All Seminars

Title: TBD
Seminar: Algebra
Speaker: Manami Roy of Fordham University
Contact: Andrew Kobin, ajkobin@emory.edu
Date: 2023-04-11 at 4:00PM
Venue: MSC W301
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Abstract:
TBD
Title: TBD
Seminar: Algebra
Speaker: Roy Joshua of Ohio State University
Contact: Parimala Raman, parimala.raman@emory.edu
Date: 2023-04-04 at 4:00PM
Venue: MSC W301
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Abstract:
TBD
Title: TBD
Seminar: Algebra
Speaker: Sameera Vemulapalli of Princeton University
Contact: Andrew Kobin, ajkobin@emory.edu
Date: 2023-03-28 at 4:00PM
Venue: MSC W301
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Abstract:
TBD
Title: TBD
Seminar: Algebra
Speaker: Thomas Brazelton of University of Pennsylvania
Contact: Andrew Kobin, ajkobin@emory.edu
Date: 2023-02-21 at 4:00PM
Venue: MSC W301
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Abstract:
TBD
Title: TBD
Seminar: Algebra
Speaker: Robert Lemke Oliver of Tufts University
Contact: Andrew Kobin, ajkobin@emory.edu
Date: 2023-02-14 at 4:00PM
Venue: MSC W301
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Abstract:
TBD
Title: Local-global principles over semi-global fields and applications to a generalized period-index problem
Seminar: Algebra
Speaker: Julia Hartmann of University of Pennsylvania
Contact: Parimala Raman, parimala.raman@emory.edu
Date: 2023-02-07 at 4:00PM
Venue: MSC W301
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Abstract:
It is a classical problem to relate the period and index of a Brauer class. Over semi-global fields, i.e., function fields over complete discretely valued fields, local-global principles have been a powerful tool in answering this question. In this talk, we consider an analog of the period-index problem for higher cohomology classes in place of Brauer classes. (Joint work with David Harbater and Daniel Krashen.)
Title: Minimal triangulations of manifolds
Job Talk: Combinatorics
Speaker: Sergey Avvakumov, Postdoctoral Fellow of University of Toronto
Contact: Liana Yepremyan, liana.yepremyan@emory.edu
Date: 2023-02-01 at 10:00AM
Venue: MSC W301
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Abstract:
Multiple results on face-vectors (numbers of faces of all dimension) of polytopes can be generalized to triangulated manifolds. They give good bounds on the number of facets. To the contrary, very little is known about the number of vertices in manifolds triangulations. I will describe how methods from combinatorics, topology, and metric geometry can tackle this problem yielding both new lower and upper bounds. Our go-to examples are going to be the n-dimensional real projective space and the n-dimensional torus.
Title: Convexity, color avoidance, and perfect hash codes
Seminar: Combinatorics
Speaker: Cosmin Pohoata of Institute of Advanced Study
Contact: Liana Yepremyan, liana.yepremyan@emory.edu
Date: 2023-01-31 at 4:00PM
Venue: MSC E408
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Abstract:
In this (informal) talk, I will discuss some favorite open problems which are related in some way or another with the Erd?s-Szekeres problem and the polynomial method.
Title: Plank Problems: Discrete Geometry and Convexity
Job Talk: Combinatorics
Speaker: Alexander Polyanskii, Senior Research Fellow of MIPT
Contact: Liana Yepremyan, liana.yepremyan@emory.edu
Date: 2023-01-27 at 10:00AM
Venue: https://emory.zoom.us/j/7744657281?pwd=TTFuLzYrVVUybkY4UlNmY0NINXNqdz09
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Abstract:
What is the smallest combined width of planks that cover a given convex region in the plane? What happens in higher dimensions? In the 50s, Thoger Bang answered this innocent question of Alfred Tarski and opened a box with many deceptively simple-looking problems. In my talk, I will overview progress in the area and its connection with other fields: theoretical computer science, number theory, and analysis. In particular, I will discuss a joint work with Zilin Jiang confirming Fejes Toth's long-standing zone conjecture and recent results with Alexey Glazyrin and Roman Karasev on a polynomial plank problem, a far-reaching generalization of Bang's theorem.
Title: Continuous Combinatorics and Natural Quasirandomness
Job Talk: Combinatorics
Speaker: Leonardo Nagami Coregliano, Postdoctoral Memb of Institute for Advanced Study
Contact: Liana Yepremyan, liana.yepremyan@emory.edu
Date: 2023-01-26 at 10:00AM
Venue: MSC W201
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Abstract:
The theory of graph quasirandomness studies graphs that "look like" samples of the Erd?s--Rényi random graph $G_{n,p}$. The upshot of the theory is that several ways of comparing a sequence with the random graph turn out to be equivalent. For example, two equivalent characterizations of quasirandom graph sequences is as those that are uniquely colorable or uniquely orderable, that is, all colorings (orderings, respectively) of the graphs "look approximately the same". Since then, generalizations of the theory of quasirandomness have been obtained in an ad hoc way for several different combinatorial objects, such as digraphs, tournaments, hypergraphs, permutations, etc. The theory of graph quasirandomness was one of the main motivations for the development of the theory of limits of graph sequences, graphons. Similarly to quasirandomness, generalizations of graphons were obtained in an ad hoc way for several combinatorial objects. However, differently from quasirandomness, for the theory of limits of combinatorial objects (continuous combinatorics), the theories of flag algebras and theons developed limits of arbitrary combinatorial objects in a uniform and general framework. In this talk, I will present the theory of natural quasirandomness, which provides a uniform and general treatment of quasirandomness in the same setting as continuous combinatorics. The talk will focus on the first main result of natural quasirandomness: the equivalence of unique colorability and unique orderability for arbitrary combinatorial objects. Although the theory heavily uses the language and techniques of continuous combinatorics from both flag algebras and theons, no familiarity with the topic is required as I will also briefly cover all definitions and theorems necessary. This talk is based on joint work with Alexander A. Razborov.