Graduate Student Colloquium
Graduate Student Colloquium
2021-2022
2021-2022
The Graduate Student Colloquium is geared towards introducing graduate students to different areas of mathematics. Each week a different member of the Graduate Center Mathematics Department faculty will discuss a topic that is accessible to all graduate students. All graduate students without an advisor are required to attend, but even those with an advisor are welcome!
All meetings of the Graduate Student Colloquium will be held on Mondays from 4:00-6:00 PM in person at the Graduate Center Room 6417, unless otherwise stated.
Organizers:
Sayantika Mondal : smondal@gradcenter.cuny.edu
Ajmain Yamin: ayamin@gradcenter.cuny.edu
Monika Cooney: mcooney@gradcenter.cuny.edu
Professor Ara Basmajian: abasmajian@gc.cuny.edu
Speaker: Dragomir Saric
Title: Quasiconformal maps, hyperbolic metric and Teichmüller spaces
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Speaker: John Terilla
Title: Machine learning and mathematical structures in natural language
Abstract: Last year, in the pizza seminar, I spoke about mathematical structures in natural language. I’d like to discuss some of those ideas again, which are now more developed and simpler. I’ll make an effort to make the talk interesting to both people that saw my talk last year and people that didn’t. I’ll begin with a little theory about machine learning, so that will be different. And it will be a chalk talk this time instead of on zoom, so I hope for some lively in-person audience engagement.
Speaker: Martin Bendersky
Title: A quick trip through the homotopy groups of the spheres
Abstract: The talk will be an introduction to some of the aspects and applications of the homotopy groups of spheres. I will use the talk as an opportunity to discuss spectral sequences, the main tool used to compute the homotopy groups of spheres.
To quote David Eisenbud:
"The subject of spectral sequences is elementary, but the notion of a bigraded spectral sequence involves so many objects and indices that it seems at first repulsive."
By the end of the talk we may decide that David was perceptive, but perhaps a bit too harsh.
Speaker: Megan owen
Title: The geometric space of phylogenetic trees
Abstract: A phylogenetic tree represents the evolutionary history of a set of organisms, like marsupials or virus strains. Billera, Holmes, and Vogtmann defined a moduli space of metric trees to provide a natural geometric setting for analyzing phylogenetic tree data. This treespace is CAT(0), or non-positively curved, allowing algorithms to quickly compute distances and Frechet means. I will discuss some recent algebraic, combinatorial, and statistical results on the space, as well as some open problems.
Speaker: Jason Behrstock
Title: Random graphs and geometric group theory
Abstract: Erdos and Renyi introduced a model for studying random graphs of a given density and proved that there is a sharp threshold at which lower density random graphs are disconnected and higher density ones are connected. I'll describe this random graph model and how it can be used to produce an interesting model for random groups from which we can learn interesting geometric information about groups via combinatorial and probabilistic techniques.
Speaker: Rohit Parikh
Title: How Mathematics can help us understand the social world.
Abstract: Two (among many) Nobel prize winners in Economics graduated from CUNY - CCNY. Both had bachelor's degrees in mathematics. The two are Kenneth Arrow, a giant in social choice, and Robert Aumann, a giant in game theory. Aumann, much more than Arrow, has been involved in the use of knowledge - epistemic logic - than Arrow. His paper Agreeing to Disagree has been cited more than 3500 times and has influenced much research at the CUNY Graduate Center.
We will talk about epistemic logic, a modal logic taking after Saul Kripke (one of our GC professors) and the way it enters into defining rationality, both in decision making and
in strategic actions when other players are involved. Work done by CUNY graduate students with doctorates in math, CS and philosophy will be described.
What is Common Knowledge? What should we (truthfully) tell people when we want to influence their actions? Did Shakespeare make use of epistemic reasoning?
How should a candidate speak when she wants to influence the voters in her favor?
This will be more of a bird's eye view talk but we will give details of some of the easier proofs.
Speaker: Victor Pan
Title: Polynomial equation and Cauchy integrals
Abstract: Solution of a polynomial equation was the central problem of mathematics for ≈ 4,000 years, from ≈ 2000 B.C. to ≈ 1850 A.D. The roots cannot be expressed through the coefficients rationally or even with radicals unless the polynomial has degree less than 2 or 5, respectively (Ruffini-Abel), but can be approximated, and this task has begun a new life with the advent of modern computers. Among hundreds of efficient techniques and algorithms, two are nearly optimal, namely, the divide and conquer one of [4] and the Quad-tree (subdivision) iterations of [1], proposed by Herman Weyl in [6] and advanced by many authors. By using Cauchy integrals we have just obtained its dramatic improvement in the important cases where an input polynomial is given by a subroutine for its evaluation rather than by its coefficients as well as where it is sparse.
Speaker: Adam Sheffer
Title: Polynomial Methods: A New Toolkit for Mathematicians
Abstract: Starting 2009, a new set of mathematical proof techniques has been developing. This set of techniques is now called Polynomial Methods. Since their inception, polynomial methods have led to a constant stream of major breakthroughs, including solutions to the finite field Kakeya conjecture, the cap set conjecture, Erdos's distinct distances problem, and a lot more.
This is a brief and elementary introduction to polynomial methods. It can also be seen as shameless advertising of the speaker's new book on the subject.
Speaker: Christian Wolf
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Speaker: Shirshendu Chatterjee
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Speaker: Alexey Ovchinnikov
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Speaker: Ara Basmajian
Title: Counting reciprocal geodesics on the modular surface
Abstract: The matrix group PSL(2,Z) acts properly discontinuously and isometrically (with respect to the hyperbolic metric) on the upper half-plane. The quotient, known as the modular surface X, is a punctured sphere with cone points of orders 2 and 3. The modular surface can be realized geometrically as two isometric hyperbolic triangles each with angles pi/2, pi/3, and 0 glued along their common edges. A reciprocal geodesic on X is a geodesic that starts and ends in the order two cone point. In this talk, after setting up the basics and defining combinatorial length of a geodesic, we count the number of reciprocal geodesics of length less than L.
Date: Monday, September 20, 2021
Speaker: Christina Sormani
Title: When do sequences of metric spaces converge?
Abstract: A light introduction to the convergence of sequences of metric spaces including research by some students who are now at the CUNY Graduate Center. Students interested in learning more after this talk may wish to watch my course presented at the Fourier Institute this past summer which can be found on my page under Teaching Summer 2021. The Fourier Institute Summer School also had a course on Riemannian Geometry.
Date: Monday, September 27, 2021
Speaker: Jack Hanson
Title: Random metrics and random growth
Abstract: Many interesting recent developments in mathematics have come from the study of stochastic growth models. These models come in many forms, including graphs with random edge lengths, diffusing particles attaching to a surface, and cellular automata. Many growth models have deep connections to differential equations, combinatorics, and representation theory. We will discuss a few canonical examples and some results and questions about them.
Date: Monday, October 4, 2021
Speaker: Ivan Horozov
Title: Arithmetic groups and modular forms
Abstract: A classical example of an arithmetic group is SL(2,Z) - the groups of 2x2 invertible matrices with integer coefficients and determinant 1. It is often called the modular group. Modular forms are functions with good properties under transformation by the modular group. They have been a central topic in number theory since Jacobi and Ramanujan. For instance the proof by Andrew Wiles of the Fermat's last Theorem is actually reduced to a theorem about modular forms, namely, Taniama-Shimura conjecture, which stated that every elliptic curve is modular)
Analogues of the modular group are the arithmetic groups SL(3,Z), SL(4,Z), Sp(4,Z). The corresponding objects of modular forms associated with them are called automorphic forms. (For the symplectic group it is called Siegel modular forms.)
Theoretically most spaces of modular forms or automorphic forms are something called a cohomology of an arithmetic group. Familiarity with it is not assumed! This is a linearization of an arithmetic group. For instance, classical modular forms are the first cohomology of SL(2,Z) with certain coefficients - H^1(SL(2,Z),V).
Part of my research is computing cohomology of arithmetic groups. Besides application to modular forms, sometimes it has application to multiple zeta values, MZVs. MZVs is another topic of my research. The talk will be centered around arithmetic groups rather than MZVs.
Date: Monday, October 18, 2021
Speaker: Artemov Sergei
Title: TBA
Abstract: TBA
Date: Monday, October 25, 2021
Speaker: Vladimir Shpilrain
Title: TBA
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Date: Monday, November 1, 2021
Speaker: Mahmoud Zeinalian
Title: TBA
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Date: Monday, November 8, 2021
Speaker: Ilya Kapovich
Title: Groups as geometric objects
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Date: Monday, November 15, 2021
Speaker: Enrique Pujals
Title: TBA
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Date: Monday, November 22, 2021
Speaker: Sandra Kingan
Title: TBA
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Date: Monday, November 29, 2021
Speaker: Melvyn Nathanson
Title: TBA
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Date: Monday, December 6, 2021
Speaker: Van Steirteghem Bart
Title: TBA
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Date: Monday, December 13, 2021
Speaker: Alexey Ovchinnikov
Title: TBA
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