All Seminars

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Title: An Effective Log-Free Zero Density Estimate for Automorphic $L$-functions and the Sato-Tate Conjecture
Seminar: Algebra
Speaker: Jesse Thorner of Emory
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-31 at 4:00PM
Venue: W304
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Abstract:
The classical techniques used to put primes in intervals of the form $[x,2x]$ are insufficient to put primes in intervals of the form $[x,x+x^{1-\delta}]$ for any $\delta>0$, or to find the least prime in an arithmetic progression $a\bmod q$. Such problems are easily answered assuming the Generalized Riemann Hypothesis, but they can be answered unconditionally using very detailed information about the location and density of zeros of Dirichlet $L$-functions in regions of the critical strip. We will discuss effective results on the distribution of general automorphic $L$-functions in the critical strip and use these distribution results to study generalizations of the aforementioned problems in the context of the Sato-Tate Conjecture.
Title: Involutions, odd degree extensions and generic splitting
Seminar: Algebra
Speaker: Anne Queguiner-Mathieuem of Universite Paris
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-26 at 3:00PM
Venue: W303
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Abstract:
Let $q$ be a quadratic form over a field $F$, and let $L$ be an odd-degree field extension of $F$. A classical theorem, known as Springer's theorem, asserts that if $q$ is isotropic (resp. hyperbolic) after scalar extension to $L$, it actually is isotropic (resp. hyperbolic) over the base field. One may ask whether a similar result holds for algebras with involution. In the talk, we will survey known results on this question, and explain the relation with the study of isotropy and hyperbolicity over some relevant function fields. New low degree results will also be included.
Title: Comparison of compactifications of modular curves
Seminar: Algebra
Speaker: Andrew Niles of Holy Cross
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-24 at 4:00PM
Venue: W304
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Abstract:
Modular curves and their compactifications are of fundamental importance in number theory. A key property of modular curves is that they are moduli spaces: their points classify certain geometric objects (elliptic curves equipped with level structure). Similarly, it was shown by Deligne-Rapoport that compactified modular curves may be viewed as moduli spaces for "generalized" elliptic curves equipped with level structure.\\ \\ It was shown by Abramovich-Olsson-Vistoli that modular curves naturally lie inside certain complicated moduli spaces, classifying "twisted stable maps" to certain algebraic stacks. These moduli spaces turn out to be complete, so the closure of a modular curve inside such a moduli space gives a compactification of the modular curve. In this talk I explain how these new compactifications can themselves be viewed as moduli spaces, and I compare them to the "classical" compactified modular curves considered by Deligne-Rapoport.
Title: Recent progress on diamond-free families
Seminar: Combinatorics
Speaker: Ryan Martin of Iowa State University
Contact: Dwight Duffus, Dwight@mathcs.emory.edu
Date: 2015-03-23 at 4:00PM
Venue: W302
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Abstract:
In the Boolean lattice, a diamond is a subposet of four distinct subsets $A, B, C, D$ such that $A \subset B, C$ and $D \supset B, C$. One of the most well-studied problems in extremal poset theory is determining the size of the largest diamond-free family in the $n$-dimensional Boolean lattice. We will discuss some recent progress on this problem.
Title: The Li-Yau Inequality and the Geometry of Graphs
Seminar: Combinatorics
Speaker: Paul Horn of The University of Denver
Contact: Dwight Duffus, Dwight@mathcs.emory.edu
Date: 2015-03-19 at 4:00PM
Venue: W303
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Abstract:
Understanding how local graph parameters, such as degree, are related to global graph properties, such as diameter and the containment of certain subgraphs, is a key aim of extremal graph theory. In the continuous setting of Riemannian manifolds, curvature serves as such a local parameter which is known to provide strong control of global structure. In this talk, we describe a new notion of curvature for graphs which, similar to in the continuous setting, strongly controls global geometric properties of a graph. In particular, it allows us to prove a discrete analogue of the Li-Yau inequality which, in this setting, controls the rate of diffusion of the continuous time random walk on a graph and which can be used to understand many further graph properties.
Title: Mock theta functions and quantum modular forms
Seminar: Algebra
Speaker: Larry Rolen of University of Cologne
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-17 at 4:00PM
Venue: W304
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Abstract:
In this talk, I will describe several related recent results related to mock theta functions, which are functions described by the Indian mathematician Ramanujan shortly before his death in 1920. These functions have very recently been understood in a modern framework thanks to the work of Zwegers and Bruinier-Funke. Here, we will revisit the original writings of Ramanujan and look at his original conception of these functions, which gives rise to a surprising picture connecting important objects such as generating functions in combinatorics and quantum modular forms.
Title: Interactive Machine Learning Across Domains
Colloquium: N/A
Speaker: Lev Reyzin of University of Illinois at Chicago
Contact: Vaidy Sunderam, vss@emory.edu
Date: 2015-03-16 at 4:00PM
Venue: W303
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Abstract:
Interactive learning algorithms have the power to engage with their data and can overcome many limitations of their passive counterparts. In this talk, I will present new algorithms and new models that I have developed for interactive learning. These results include the development of new pool-based, bandit, and query learners. I will also discuss applications and future research challenges for interactive machine learning settings, focusing on the life sciences.
Title: Algebraic Preconditioning of Symmetric Indefinite Systems
Seminar: Numerical Analysis and Scientific Computing
Speaker: Miroslav Tuma of Academy of Sciences of the Czech Republic
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2015-03-10 at 4:00PM
Venue: W301
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Abstract:
Sparse symmetric indefinite linear systems of equations arise in many practical applications. An iterative method is frequently the method of choice to solve such systems but a system transformation called preconditioning is often required for the solver to be effective. In the talk we will deal with development of incomplete factorization algorithms that can be used to compute high quality preconditioners. We will consider both general indefinite systems and saddle-point problems. Our approach is based on the recently adopted limited memory approach (based on the work of Tismenetsky, 1991) that generalizes recent work on incomplete Cholesky factorization preconditioners. A number of new ideas are proposed with the goal of improving the stability, robustness and efficiency of the resulting preconditioner. For general indefinite systems, these include the monitoring of stability as the factorization proceeds and the use of pivot modifications when potential instability is observed. Numerical experiments involving test problems arising from a range of real-world applications are used to demonstrate the effectiveness of our approach and comparisons are made with a state-of-the-art sparse direct solver. The talk will be based on joint work with Jennifer Scott, Rutherford Appleton Laboratory.
Title: Zero-cycles and rational points on rationally connected varieties, after Harpaz and Wittenberg
Seminar: Algebra
Speaker: Jean-Louis Colliot-Thelene of Universite Paris-Sud
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-03-03 at 4:00PM
Venue: W304
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Abstract:
Harpaz and Wittenberg have recently proved a general result on the local-global principle for zero-cycles on rationally connected varieties. There is also a conditional variant for rational points. I shall explain some of the ideas in their paper. Reference : http://arxiv.org/abs/1409.0993
Title: Extracting medically interpretable concepts from complex health data
Colloquium: N/A
Speaker: Joyce Ho of University of Texas at Austin
Contact: Vaidy Sunderam, vss@emory.edu
Date: 2015-03-03 at 4:00PM
Venue: W303
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Abstract:
Electronic health records (EHRs) are an increasingly important source of patient information. Efficient analysis of EHRs can help address many healthcare problems by improving clinical decisions, facilitating knowledge discoveries, and enabling the development of cost-effective treatment and management programs. However, EHRs pose many formidable challenges for traditional analytics. The data are collected across diverse populations, consist of heterogeneous and noisy information, and have varying time resolutions. Moreover, healthcare professionals are unaccustomed to interpreting high-dimensional EHRs; they prefer concise medical concepts. Thus, a major question is how to transform EHR into meaningful concepts with modest levels of expert guidance.\\ \\ In this talk, I will discuss two approaches to extract concise, meaningful concepts from certain types of health datasets. First, I will describe a dynamic time series model that tracks a patient's cardiac arrest risk based on physiological measurements (i.e., heart rate, blood pressure, etc.) in an intensive care unit. Our algorithm is inspired by financial econometric and yields interpretability and predictability of a cardiac arrest event. Next, I will present a sparse, nonnegative tensor factorization model to obtain multiple medical concepts with minimal human supervision. Tensor factorization utilizes information in the multiway structure to derive concise latent factors even with limited observations. We applied tensor analysis to real EHRs from the Geisinger Health System to automatically identify relevant medical concepts. Both our models are powerful and data-driven approaches to extract medically interpretable concepts from complex health data.