# All Seminars

Title: Local-global principle for hermitian spaces over semi-global fields
Defense: Dissertation
Speaker: Jayanth Guhan of Emory University
Contact: Jayanth Guhan, jayanth.guhan@emory.edu
Date: 2022-06-20 at 11:00AM
Venue: MSC E408
Abstract:
Title: Counting rational points on some moduli stacks or if that sounds scary on some modular curves
Seminar: Algebra
Speaker: Jordan Ellenberg of University of Wisconsin, Madison
Contact: David Zureick-Brown, david.zureick-brown@emory.edu
Date: 2022-04-29 at 2:00PM
Venue: MSC W301
Abstract:
How many elliptic curves are there which have a cyclic N-isogeny? You may note that this question is not very carefully stated. I will talk about the surprisingly subtle issue of how this question should best be precisely posed, and talk about recent work in this direction and related ones due to Rob Harron and Andrew Snowden, Brendan Boggess and Soumya Sankar, Maggie Pizzo + Carl Pomerance + John Voight, Tristan Phillips, John Yin, and to some extent the speaker + Matt Satriano + David Zureick-Brown.
Title: Relative Arbitrage Opportunities in Stochastic Games and its Numerical Scheme
Seminar: Computational Math
Speaker: Nicole Yang of Morgan Stanley
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2022-04-28 at 10:00AM
Venue: Virtual (RSVP by email to lruthotto@emory.edu)
Abstract:
The Relative arbitrage portfolio outperforms a market portfolio over a given time horizon with probability one. When an investor competes with both market and peers, does relative arbitrage opportunity exist? What is the best performance one can achieve? What is the impact on the market when a large group of investors competes in a similar way? We construct a framework of multi-agent optimization for relative arbitrage problems to answer these questions. Under a dynamical system with interacting investors, the objective is characterized by the smallest non-negative continuous solution of the Cauchy problem for the associated partial differential equation. We solve the optimal strategies by deriving the Nash equilibrium in finite player and mean field games. However, solving this numerically presents many challenges due to the non-uniqueness and the curse of dimensionality. We provide a deep learning approach to tackle minimal solutions in the high-dimensional PDEs based on the associated obstacle problem and Deep Galerkin Method. We show that the minimal deep learning based solution is a good approximation in the volatility-stabilized models when compared to the grid-based numerical solution. We lay out a few future research topics related to deep learning, mean field type problems, and inverse problems.
Title: Half Covering, Half Coloring
Defense: Dissertation
Speaker: Alexander Clifton of Emory University
Contact: Alexander Clifton, alexander.james.clifton@emory.edu
Date: 2022-04-22 at 10:30AM
Venue: MSC W307C
Abstract:
We will discuss two types of problems in extremal combinatorics. First, we discuss problems about covering sets of points using affine hyperplanes. We consider a higher multiplicity generalization of a result of Alon and F\"{u}redi about the minimum number of hyperplanes needed to cover all but one vertex of an $n$-cube. We then discuss related covering problems for triangular grids. Next, we answer a question in arithmetic Ramsey theory. For a fixed set $D$, of positive integers, let $\Delta(D,k;2)$ be the smallest $N$ such that any $2$-coloring of $\{1,2,\cdots,N\}$ contains a monochromatic sequence $a_1 Title: Directed Reading Program presentations II Type: N/A Speaker: Several Undergraduates of Emory University Contact: Chris Keyes, christopher.keyes@emory.edu Date: 2022-04-21 at 2:30PM Venue: Psychology and Interdisciplinary Sciences Building: PAIS 280 (tentative) Abstract: Join us to celebrate the conclusion of the Spring 2022 Directed Reading Program! Students will give short presentations on what they learned, covering a wide range of topics in pure and applied mathematics. \\ \textbf{Speakers and topics for part II}: \begin{enumerate} \item Michael Liu, \emph{Percolation theory} (Mentor: Alexander C.) \item Catherine Baker, \emph{Numerical analysis} (Mentor: Riti) \item Judy Hao, \emph{Partial differential equations} (Mentor: Ben) \item Cecilia Garcia and Siwei Xu, \emph{Computational algebra} (Mentor: Alex D.) \end{enumerate} Title: Directed Reading Program presentations I Type: N/A Speaker: Several Undergraduates of Emory University Contact: Chris Keyes, christopher.keyes@emory.edu Date: 2022-04-19 at 4:00PM Venue: MSC W303 Abstract: Join us to celebrate the conclusion of the Spring 2022 Directed Reading Program! Students will give short presentations on what they learned, covering a wide range of topics in pure and applied mathematics. \\ \textbf{Speakers and topics for part I}: \begin{enumerate} \item Hayden Truong, \emph{Commutative algebra} (Mentor: Ariella) \item Meg Ruder, \emph{Number theory} (Mentor: Shilpi) \item Ezra Arovas, \emph{Sports analytics} (Mentor: Chris) \item Zoe Ji, \emph{Math for computer graphics} (Mentor: Abbey) \end{enumerate} Title: Ranking Instagram Preferences: Get to know your friends better through experimental mathematics Defense: Honors Thesis Speaker: Urshila Choubal of Emory University Contact: Urshila Choubal, urshila.vikram.choubal@emory.edu Date: 2022-04-07 at 10:00AM Venue: MSC E406 Abstract: Ranking methods offer remarkable potential in creating and revamping recommendation systems. The task of suggesting relevant and attractive content to users is directly benefited by improving ranking techniques. With graph ranking as the mathematical foundation on which recommendation systems are built, vertex prestige is a critical problem to be addressed. Several models exist that rank vertices in a graph. However, we explore the following methods: HITS, Dominant Eigenvector, and PageRank. We aim to emulate a recommendation system by first gathering primary data from Instagram by tracking the activity of nine participants on the app. With the help of the three ranking methods, we intend to provide our recommendation to the participants based on having accessed their past preferences. Title: Residue on affine Grasmannians Seminar: Algebra Speaker: Philippe Gille of CNRS, Université Lyon 1 Contact: David Zureick-Brown, dzureic@emory.edu Date: 2022-04-05 at 4:00PM Venue: MSC W303 Abstract: This is a report on joint work with Mathieu Florence. For an affine algebraic group$G/k$, we will explain how a non integral point of$G( k((t)) )$gives rise to a homomorphism$H \to G$where$H$is either the additive group or the multiplicative group. Title: Forbidden subgraphs and spherical two distance sets Seminar: Discrete Math Speaker: Zilin Jiang of Arizona State University Contact: Liana Yepremyan, liana.yepremyan@EMORY.EDU Date: 2022-04-01 at 4:00PM Venue: MSC W303 Abstract: Given a real number $\lambda$, what can we say about the family G($\lambda$) of graphs with eigenvalues bounded from below by -$\lambda$The Cauchy interlacing theorem implies that that the family G($\lambda$) is closed under taking (induced) subgraphs. Similar to Wagner’s theorem, which describes the family of planar graphs by finite forbidden minors, it is natural to ask for which $\lambda$ the family G($\lambda$) has a finite forbidden subgraph characterization. In this talk, I will illustrate the key ideas in answering this question, and I will demonstrate a peculiar connection to spherical two distance sets — a set of unit vectors in a Euclidean space the pairwise inner products of which assume only two values. Joint work with Alexandr Polyanskii, Jonathan Tidor, Yuan Yao, Shengtong Zhang and Yufei Zhao. Title: The Georgia Algebraic Geometry Symposium Seminar: Algebra Speaker: {} of Contact: David Zureick-Brown, david.zureick-brown@emory.edu Date: 2022-04-01 at 5:00PM Venue: MSC E208 Abstract: The Georgia Algebraic Geometry Symposium is a conference series, jointly organized by the University of Georgia, Emory University and Georgia Tech. \\ The conference will begin Friday late afternoon and end Sunday early afternoon. \\ See {https://www.math.emory.edu/$\sim\$ dzb/conferences/GAGS2022/} for more information. \\ Speakers: \\ Evangelia Gazaki (University of Virginia) \\ Roman Fedorov (University of Pittsburgh)\\ Angela Gibney (University of Pennsylvania)\\ Philippe Gille (Institut Camille Jordan)\\ Diego Izquierdo (École Polytechnique)\\ Martin Olsson (University of California, Berkeley)\\ Karl Schwede (University of Utah)\\ Brooke Ullery (Emory University)\\