All Seminars
| Title: Question Answering with User Generated Content |
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| 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 |
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| 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 |
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| 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: |
| Title: Primality Testing and Integer Factorization Using Elliptic Curves |
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| 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: MSC 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 |
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| Seminar: Combinatorics |
| Speaker: Boris Bukh of Carnegie Mellon University |
| Contact: Dwight Duffus, dwight@mathcs.emory.edu |
| Date: 2017-04-05 at 4:00PM |
| Venue: MSC 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 |
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| 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 |
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| Defense: Masters |
| Speaker: Ethan Alwaise of Emory University |
| Contact: Ethan Alwaise, ethan.alwaise@emory.edu |
| Date: 2017-04-05 at 5:30PM |
| Venue: MSC 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 |
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| 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 |
| Title: Zero-Cycles on Torsors under Linear Algebraic Groups |
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| Defense: Dissertation |
| Speaker: Reed Sarney of Emory University |
| Contact: Reed Sarney, rlgordo@emory.edu |
| Date: 2017-04-03 at 1:00PM |
| Venue: MSC W303 |
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| Abstract: Let $k$ be a field, let $G$ be a smooth connected linear algebraic group over $k$, and let $X$ be a $G$-torsor. Totaro asked: if $X$ admits a zero-cycle of degree $d$, does $X$ have a closed {\'e}tale point of degree dividing $d$? We give a positive answer in two cases: \begin{enumerate} \item $G$ is an algebraic torus of rank $\leq 2$ and $\textup{ch}(k)$ is arbitrary, and \item $G$ is an absolutely simple adjoint group of type $A_1$ or $A_{2n}$ and $\textup{ch}(k) \neq 2$. \end{enumerate} We also present the first known examples where Totaro's question has a negative answer. |
| Title: Rank-Favorable Bounds for Rational Points on Superelliptic Curves |
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| Defense: Master's |
| Speaker: Noam Kantor of Emory University |
| Contact: Noam Kantor, noam.kantor@emory.edu |
| Date: 2017-04-03 at 3:00PM |
| Venue: MSC: N304 |
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| Abstract: Let $C$ be a curve of genus at least two, and let $r$ be the rank of the rational points on its Jacobian. Under mild hypotheses on $r$, recent results by Katz, Rabinoff, Zureick-Brown, and Stoll bound the number of rational points on $C$ by a constant that depends only on its genus. Yet one expects an even stronger bound that depends favorably on $r$: when $r$ is small, there should be fewer points on $C$. In a 2013 paper, Stoll established such a ``rank-favorable" bound for hyperelliptic curves using Chabauty's method. In the present work we extend Stoll's results to superelliptic curves. We also discuss a possible strategy for proving a rank-favorable bound for arbitrary curves based on the metrized complexes of Amini and Baker. Our results have stark implications for bounding the number of rational points on a curve, since $r$ is expected to be small for ``most" curves. |