All Seminars

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Title: Congruences from quaternion algebras
Seminar: Algebra
Speaker: Kimball Martin of University of Oklahoma
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-11-07 at 4:00PM
Venue: W306
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Abstract:
Studying congruences between modular forms is a prosperous avenue in number theory. One approach to obtaining congruences involves computations on the Jacobian (Mazur, Ribet, ...). For instance, Mazur uses the Jacobian to determine when there is a weight 2 cusp form of prime level congruent to an Eisenstein series, which has various applications. We will explore another approach to obtaining congruences of modular forms using the arithmetic of quaternion algebras and the Jacquet-Langlands correspondence. This will lead to (1) generalizations work of Mazur and Ribet on weight 2 Eisenstein congruences, and (2) a phenomenon of many mod 2 congruences between weight k cusp forms.
Title: Extremal number of configurations in a grid
Seminar: Combinatorics
Speaker: Marcelo Sales of University of Sao Paulo
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-11-06 at 4:00PM
Venue: W302
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Abstract:
A configuration is a finite set of points with no three collinear. Two configurations have the same order type if there exists a bijection between these two configurations that preserves the orientation of every ordered triple. A configuration A contains a copy of a configuration B some subset of A has the same order type of B and we denote by B \subset A. For a configuration B and an integer m, the extremal number ex(m,B)= max {|A| : B is not a subset of A, A \subset [m]^2} is the maximum size of a subset of the grid $[m]^2$ without a copy of $B$. We discuss some bounds on this function for general B.
Title: Insights from computational fluid dynamic modelling for aortic arch pathologies
Seminar: Numerical Analysis and Scientific Computing
Speaker: Massimiliano Marrocco-Trischitta of San Donato Hospital in Milan, Italy
Contact: Adrien Lefieux, adrien.lefieux@emory.edu
Date: 2017-11-03 at 2:00PM
Venue: W301
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Abstract:
Objectives. To assess whether the geometrical and hemodynamic reappraisal of the IshimaruÂ’s Aortic Arch Map according to Aortic Arch Classification in Type I, II, and III, may provide valuable information regarding the suitability for thoracic endovascular aortic repair (TEVAR), and the risk of aortic dissection. Methods. Anonymized thoracic computed tomography scans of healthy aortas were reviewed, and stratified according to the Aortic Arch Classification. Twenty patients of each Type of Arch were selected. Further processing allowed calculation of angulation and tortuosity of each proximal landing zones. Data were described indicating both proximal landing zone and Type of Arch (e.g. 0/I). Also, among these 60 CT angiography scans, 15 were selected, 5 per Type of Arch, for further analysis. Computational fluid dynamics were performed to compute displacement forces, exerted by pulsatile blood flow on the aortic wall in the defined landing areas. Equivalent surface tractions were computed dividing the displacement forces magnitude of each proximal landing zone by the corresponding area. The three-dimensional orientation (x,y,z) of displacement forces was described as an upward (z direction), and a sideways component (x-y plane).
Title: Improving Question Answering by Bridging Linguistic Structures and Statistical Learning
Defense: Dissertation
Speaker: Tomasz Jurczyk of Emory University
Contact: TBA
Date: 2017-11-02 at 4:00PM
Venue: W301
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Abstract:
Question answering (QA) has lately gained lots of interest from both academic and industrial research. No matter the question, search engine users expect the machines to provide answers instantaneously, even without searching through relevant websites.\\ \\While a significant portion of these questions ask for concise and well known facts, more complex questions do exist and they often require dedicated approaches to provide robust and accurate systems.\\ \\This thesis explores linguistically-oriented approaches for both factoid and non-factoid question answering and applications to cross-genre tasks. The contributions include new annotation schemes for the question answering oriented corpora, extracting linguistic structures and performing matching, and early exploration of applications to conversation dialog tasks.
Title: 576 Fermions
Seminar: Algebra
Speaker: Theo Johnson-Freyd of Perimeter Institute
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-10-24 at 4:00PM
Venue: W306
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Abstract:
The Stolz--Teichner conjectures predict that the generalized cohomology theory called Topological Modular Forms has a geometric model in terms of the space of 2-dimensional supersymmetric quantum field theories, and that holomorphic vertex operator superalgebras provide the geometric model for nontrivial degrees of TMF. Since TMF is periodic with period 576, these conjectures in particular predict an equivalence between holomorphic VOSAs of different central charge that had not been discovered by physicists. I will report on progress constructing this "periodicity" equivalence geometrically. Specifically, I will explain the solution to the warm-up problem of constructing geometrically the 8-fold periodicity of real K-theory: my solution realizes this periodicity as an example of super symplectic reduction. I will then explain why I believe the Conway group Co0 will play a role in the 576-fold periodicity problem, and why my recent computation of H^4(Co0) provides evidence for this belief.
Title: Survey on recent results on maximal tori of algebraic groups
Seminar: Algebra
Speaker: Philippe Gille of CNRS, Lyon
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-10-24 at 5:00PM
Venue: W306
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Abstract:
Prasad and Rapinchuk investigated the isopectrality problem for certain Riemannian varieties by analysing in what extent a semisimple algebraic group defined over a number field is determined by its maximal tori. We shall report advances on this topic by Chernousov/Rapinchuk/Rapinchuk, Bayer-Fluckiger/Lee/Parimala and others by discussing the case of non-archimedean fields and local-global principles.
Title: Packing nearly optimal Ramsey $R(3,t)$ graphs
Seminar: Combinatorics
Speaker: Lutz Warnke of Georgia Institute of Technology
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-10-23 at 4:00PM
Venue: W302
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Abstract:
TBA
Title: Backtracking-Based Accelerated Descent Methods for Large-Scale Linear Inverse Problems
Seminar: Numerical Analysis and Scientific Computing
Speaker: Xianqi Li of University of Florida
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2017-10-20 at 2:00PM
Venue: W301
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Abstract:
Large-scale linear inverse problems arise in a wide range of applications such as image processing and statistical inference. However, the high dimensional (possibly dense and ill-conditioned) matrix in data fidelity term often brings significantly computational challenges when solving the formulated optimization problem and hence hindered the applicability of the sophisticated interior point method and second-order optimization methods. To tackle those challenges, first-order gradient descent method turns into a good choice. In this talk, we first review some classical first-order accelerated descent methods, then introduce our proposed backtracking based accelerated descent methods, which are capable of hunting for more aggressive stepsize via conducting fewer number of line searches. A brief convergence analysis will be presented. The numerical results on structured (low rank and/or sparsity and/or group sparsity) network learning and total-variation based image reconstruction problems indicate the efficiency and effectiveness of the proposed algorithms.
Title: You Are Already Living Inside a Computer
Seminar: Computer Science
Speaker: Ian Bogost of Georgia Tech
Contact: TBA
Date: 2017-10-20 at 3:00PM
Venue: W201
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Abstract:
Futurists and philosophers have made dramatic predictions about the future of computers. Artificial intelligence might end the need for human work, or it might enslave humanity, or it might facilitate a kind of rapture into machines, where people's consciousnesses could upload and, through simulation, become immortal.\\ \\Realized or not, those future visions offer a stark contrast with the reality of computing today: One where digital machinery is embedded in the ordinary, human world rather than leading away from it. The computational aspects of ordinary things from smartphone apps to internet-connected toasters have become goals unto themselves, rather than just a means to an end. As it spreads from desktops and back-offices to pockets, cameras, cars, and door locks, the affection people have with computers transfers onto other, even more ordinary objects. And the more people love using computers for everything, the more life feels incomplete unless it takes place inside them. Reality might have beaten the futurists to the punch, by turning computing into a way of life.
Title: The density of squarefree values taken by a polynomial
Colloquium: N/A
Speaker: Manjul Bhargava of Princeton
Contact: John Duncan, john.duncan@emory.edu
Date: 2017-10-20 at 4:00PM
Venue: W201
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Abstract:
It is well known that the density of integers that are squarefree is $6/\pi^2$, giving one of the more intriguing occurrences of $\pi$ where one might not a priori expect it! A natural next problem that has played an important role in number theory is that of understanding the density of squarefree values taken by an integer polynomial. We survey a number of recent results on this problem for various types of polynomials - some of which use the ``ABC Conjecture'' and some of which do not.