All Seminars

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Title: Athens-Atlanta Joint Number Theory Seminar
Seminar: Algebra
Speaker: Gopal Prasad and Rachel Pries of University of Michigan and Colorado State University
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-04-18 at 4:00PM
Venue: Room 208
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Abstract:
Rachel Pries (4pm) \\ Title: Galois action on homology of Fermat curves \\ Abstract: We prove a result about the Galois module structure of the Fermat curve using commutative algebra, number theory, and algebraic topology. Specifically, we extend work of Anderson about the action of the absolute Galois group of a cyclotomic field on a relative homology group of the Fermat curve. By finding explicit formulae for this action, we determine the maps between several Galois cohomology groups which arise in connection with obstructions for rational points on the generalized Jacobian. Heisenberg extensions play a key role in the result. This is joint work with R. Davis, V. Stojanoska, and K. Wickelgren. \\ Gopal Prasad (5:15pm) \\ Title: Weakly commensurable Zariski-dense subgroups of semi-simple groups and isospectral locally symmetric spaces \\ Abstract. I will discuss the notion of weak commensurability of Zariski-dense subgroups of semi-simple groups. This notion was introduced in my joint work with Andrei Rapinchuk (Publ. Math. IHES 109(2009), 113-184), where we determined when two Zariski-dense S-arithmetic subgroups of absolutely almost simple algebraic groups over a field of characteristic zero can be weakly commensurable. These results enabled us to prove that in many situations isospectral locally symmetric spaces of simple real algebraic groups are necessarily commensurable. This settled the famous question "Can one hear the shape of a drum?" of Mark Kac for these spaces. The arguments use algebraic and transcendental number theory.
Title: Point Processes and Asynchronous Event Sequence Analysis
Seminar: N/A
Speaker: Hongteng Xu of Georgia Institute of Technology
Contact: TBA
Date: 2017-04-17 at 4:00PM
Venue: White Hall 112
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Abstract:
Real-world interactions among multiple entities, such as user behaviors in social networks, job hunting and hopping, and diseases and their complications, often exhibit self-triggering and mutually-triggering patterns. For example, a tweet of a twitter user may trigger further responses from her friends. A disease of a patient may trigger other complications. Temporal point processes, especially Hawkes processes and correcting processes, have a capability to capture the triggering patterns quantitatively. This talk aims to introducing basic concepts of point processes and proposing a series of cutting-edge techniques for practical applications. In particular, the Granger causality analysis of Hawkes processes, the clustering problem of event sequences, the combination of deep learning and point processes, and some interesting applications will be discussed.\\ \\ Bio: Hongteng Xu is a Ph.D. candidate in the School of Electrical and Computer Engineering, Georgia Tech, jointly supervised by Prof. Hongyuan Zha (CSE) and Prof. Mark A. Davenport (ECE). At the same time, he is a research assistant in the College of Computing at Georgia Tech. He received his Bachelor Degree in Electronic and Information Engineering from Tianjin University in 2010 and his dual Master Degree in ECE from Shanghai Jiao Tong University and Georgia Tech in 2013. His research interests include machine learning and its applications, e.g., computer vision and data mining. Currently, he has published over 20 papers on top conferences and journals.
Title: Question Answering with User Generated Content
Defense: Dissertation
Speaker: Denis Savenkov of Emory University
Contact: Denis Savenkov, denis.savenkov@emory.edu
Date: 2017-04-13 at 4:00PM
Venue: W306
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Abstract:
Modern search engines have made dramatic progress in answering many user questions, especially about facts, such as those that might be retrieved or directly inferred from a knowledge base. However, many other more complex factual, opinion or advice questions, are still largely beyond the competence of computer systems. For such information needs users still have to dig into the "10 blue links" of search results and extract relevant information. As conversational agents become more popular, question answering (QA) systems are increasingly expected to handle such complex questions and provide users with helpful and concise information. In my dissertation I develop new methods to improve the performance of question answering systems for a diverse set of user information needs using various types of user-generated content, such as text documents, community question answering archives, knowledge bases, direct human contributions, and explore the opportunities of conversational settings for information seeking scenarios.
Title: A characterization of Toric pairs
Seminar: Algebra
Speaker: Morgan Brown of University of Miami
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-04-11 at 4:00PM
Venue: W306
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Abstract:
Toric varieties are ubiquitous in algebraic geometry. They have a rich combinatorial structure, and give the simplest examples of log Calabi-Yau varieties. \\ We give a simple criterion for characterizing when a log Calabi-Yau pair is toric, which answers a case of a conjecture of Shokurov. This is joint work with James McKernan, Roberto Svaldi, and Runpu Zong.
Title: Statistical and informatics methods for analyzing next generation sequencing data
Defense: Dissertation
Speaker: Li Chen of Emory University
Contact: Li Chen, li.chen@emory.edu
Date: 2017-04-10 at 9:00AM
Venue: CNR 2001
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Abstract:
TBA
Title: Primality Testing and Integer Factorization Using Elliptic Curves
Defense: Master's Defense
Speaker: Andrew Wilson of Emory University
Contact: Andrew Wilson, andrew.wilson@emory.edu
Date: 2017-04-06 at 4:15PM
Venue: E406
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Abstract:
Testing integers for primality and factoring large integers is an extremely important subject for our daily lives. Every time we use a credit card to make online purchases we are relying on the difficulty of factoring large integers for the security of our personal information. Similar encryption methods are used by governments around the world to protect their classi ed information, stressing the importance of the subject of primality testing and factoring algorithms to both personal and national security. Elementary number theory has been a key tool in the foundation of primality testing and factoring algorithms, speci fically the work of Euler and Fermat, whose developments on modular arithmetic give us key tools that we still use today in the more complex primality tests and factoring methods. More recently people have used deeper ideas from geometry, namely elliptic curves, to develop faster tests and algorithms. In this thesis we continue this trend, and develop new primality tests that utilize previous theory of elliptic curves over nite elds. The primary point is that the points on these curves form a special group, which breaks down when working over Z/NZ, when N is not prime. Our theorems make use of the work of Kubert, Hasse, Mazur, and many more to yield a primality test that gives no false positives.
Title: Rank of matrices with few distinct entries
Seminar: Combinatorics
Speaker: Boris Bukh of Carnegie Mellon University
Contact: Dwight Duffus, dwight@mathcs.emory.edu
Date: 2017-04-05 at 4:00PM
Venue: W303
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Abstract:
Many applications of the linear algebra method to combinatorics rely on bounds on ranks of matrices with few distinct entries and constant diagonal. In this talk, I will explain some of these applications. I will also present a classification of sets \textit{L} for which no low-rank matrix with entries in \textit{L} exists.
Title: Generalized Cross Validation for Ill-Posed Inverse Problems
Defense: Honors
Speaker: Hanyong Wu of Emory University
Contact: Hanyong Wu,
Date: 2017-04-05 at 5:00PM
Venue: W306
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Abstract:
In this thesis, we will introduce two popular regularization tools for ill- posed linear inverse problem, truncated singular value decomposition and Tikhonov regularization. After that we will implement them with the gener- alized cross validation (GCV) method to choose regularization parameters. We consider in particular problems that have noise in the measured data, noise in the matrix, and noise in both the measured data and the matrix. Numerical experiments are used to test the GCV method for each of these noise models.
Title: An Algorithm for Numerically Computing Preimages of the $j$-invariant
Defense: Masters
Speaker: Ethan Alwaise of Emory University
Contact: Ethan Alwaise, ethan.alwaise@emory.edu
Date: 2017-04-05 at 5:30PM
Venue: E408
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Abstract:
Here we explore the problem of numerically computing preimages of the $j$-invariant. We present an algorithm based on studying the asymptotics of the Fourier coefficients of the logarithmic derivative of $j(\tau)$. We use recent work of Bringmann et al., which gives asymptotics for the Fourier coefficients of divisor modular forms, to identify the real and imaginary parts of the preimage.
Title: Equivariant analogs of the arithmetic of del Pezzo surfaces
Seminar: Algebra
Speaker: Alexander Duncan of University of South Carolina
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2017-04-04 at 5:00PM
Venue: W306
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Abstract:
Given an algebraic variety X over a non-closed field, one might ask if X is rational, is unirational, has a rational point, has a Zariski-dense set of rational points, or has a 0-cycle of degree 1. All of these properties have ``equivariant'' generalizations to the case where the variety has an action of algebraic group G. The corresponding properties are interesting even when the base field is algebraically closed. Moreover, one can exploit this connection to establish geometric facts using arithmetic methods and vice versa. I will outline this correspondence with an emphasis on del Pezzo surfaces. In particular, I will completely characterize the equivariant analogs of the above properties for del Pezzo surfaces of degree greater than or equal to 3 over the complex numbers. I will also discuss some partial results for degrees 1 and 2 that, despite being about complex surfaces, have arithmetic ramifications