All Seminars

Show:
Title: Finding the hidden symmetries of Nature
Seminar: Mathematical Physics
Speaker: Maria Clara Nucci of University of Perugia
Contact: Michele Benzi, benzi@mathcs.emory.edu
Date: 2016-02-10 at 4:00PM
Venue: W303
Download Flyer
Abstract:
Twenty years ago David J. Gross presented, at the National Academy of Sciences, a paper entitled "The role of symmetry in fundamental physics", which was later published in PNAS. I shall use that talk as a thread in order to illustrate my recent work related to the following main themes: (A) going from Classical to Quantum Mechanics by preserving Noether symmetries; (B) finding hidden linearity of maximally superintegrable systems; (C) determining Lagrangians (and Noether symmetries) for systems without Lagrangians. I shall provide several examples for each theme, including models in population dynamics and the Lorenz system in meteorology
Title: The Iwasawa main conjecture for elliptic curves at supersingular prime
Seminar: Algebra
Speaker: Florian Sprung of Princeton/IAS
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-02-09 at 4:00PM
Venue: W304
Download Flyer
Abstract:
Iwasawa theory is a bridge between analytic objects and algebraic objects. We give a friendly introduction to the main conjecture in the ordinary case (and define what 'ordinary' means), and then outline the supersingular (=non-ordinary) theory. The main philosophy of the proof in the supersingular case is to work with a pair of simple objects similar to the ordinary ones.
Title: Numerical techniques for multiscale dynamical systems
Seminar: Numerical Analysis and Scientific Computing
Speaker: Seong Jun Kim of Georgia Institute of Technology
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2016-02-05 at 1:00PM
Venue: W306
Download Flyer
Abstract:
The main aim of this talk is to discuss multiscale algorithms for a class of highly oscillatory dynamical systems. There had been many algorithms for computing the macroscale behavior of highly oscillatory dynamical systems with the help of microscale systems. While they achieved remarkable successes, their applications to general highly oscillatory dynamical systems are still limited. This talk will provide some of the background materials, perspectives on the current challenges as well as recent progresses with my collaborators.
Title: Chow groups with coefficients and generalized Severi-Brauer varieties
Seminar: Algebra
Speaker: Patrick McFaddin of University of Georgia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-02-02 at 4:00PM
Venue: W304
Download Flyer
Abstract:
The theory of algebraic cycles on homogenous varieties has seen many useful applications to the study of central simple algebras, quadratic forms, and Galois cohomology. Significant results include the Merkurjev-Suslin Theorem and Suslin's Conjecture, recently proved by Merkurjev. Despite these successes, a general description of Chow groups and Chow groups with coefficients remains elusive, and computations of these groups are done in various cases. In this talk, I will give some background on K-cohomology groups of Severi-Brauer varieties and discuss some recent work on computing these groups for an algebra of index 4.
Title: Indexing Moving Objects for Predictive Spatio-Temporal Queries
Defense: Dissertation
Speaker: Xiaofeng Xu of Emory University
Contact: Xiaofeng Xu, xiaofeng.xu@emory.edu
Date: 2016-01-28 at 2:30PM
Venue: W304
Download Flyer
Abstract:
The rapid development of positioning techniques has enabled information to be widely collected on continuously moving objects, such as vehicles and mobile device users. Since moving object data is large and updates frequently, database systems supporting massive updates and predictive spatio-temporal queries are essential for modern location-based services. Traditional spatial accessing or indexing mechanisms barely consider velocity information of the objects to improve query performance. In this dissertation, I present novel approaches that augment existing tree-based and grid-based indexes for moving object databases with velocity information and prove that these approaches can significantly improve query performance with comparable update performance in both in-disk and in-memory scenarios.. Predictive range query, which retrieves objects in a certain spatial region at some future time, is the most motivating type of spatio-temporal queries in real world location-based services. Different from predicting future location of a single moving object, performing predictive range queries over large moving object databases incurs much heavier computational burden, which makes efficiency as important as accuracy for real-time spatio-temporal enquiries. Motion functions, which predict future object locations based on some analytic functions, can efficiently process short-term predictive range queries, since they can be seamlessly embedded into existing indexing mechanisms. However, motion functions cannot perform long-term predictions since motions of the moving objects might change over time. Other prediction functions such as trajectory patterns and statistical graphic models are more accurate but less efficient. In this dissertation, I also present a pruning mechanism that improve the performance for long-term predictive range queries based on (high-order) Markov chain models learned from historical trajectories. The key to our approach is to devise compressed representations for sparse multi-dimensional matrices, and leverage efficient algorithms for matrix computations. We conduct experiments on both simulated and real world datasets to demonstrate that our methods gain significant improvements over other existing methods.
Title: Vector bundles on moduli space of stable curves with marked points.
Seminar: Algebra
Speaker: Anna Kazanova of University of Georgia
Contact: David Zureick-Brown, dab@mathcs.emory.edu
Date: 2016-01-26 at 4:00PM
Venue: W304
Download Flyer
Abstract:
Conformal block vector bundles are vector bundles on the moduli space of stable curves with marked points defined using certain Lie theoretic data. Over smooth curves, these vector bundles can be identified with generalized theta functions. In this talk we discuss extension of this identification over the stable curves. This talk is based on joint work with P. Belkale and A. Gibney.
Title: Auction theory and tropical geometry
Seminar: Algebra
Speaker: Josephine Yu of Georgia Tech
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2016-01-19 at 4:00PM
Venue: W304
Download Flyer
Abstract:
In a recent and ongoing work, Baldwin and Klemperer explored a connection between tropical geometry and economics. They gave a sufficient condition for the existence of competitive equilibrium in product-mix auctions of indivisible goods. This result, which we call the Unimodularity Theorem, can also be traced back to the work of Danilov, Koshevoy, and Murota. I will introduce auction theory, prove of the Unimodularity Theorem, and discuss special cases such as stable matching with transferable utility. This is based on joint work with Ngoc Mai Tran.
Title: The Riemann Hypothesis for Period Polynomials
Seminar: Algebra
Speaker: Ken Ono of Emory University
Contact: David Zureick-Brown, dab@mathcs.emory.edu
Date: 2016-01-12 at 4:00PM
Venue: W304
Download Flyer
Abstract:
TBA
Title: The 1729 K3 surface
Seminar: Algebra and Number Theory
Speaker: Sarah Trebat-Leder of Emory University
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-12-08 at 4:00PM
Venue: W304
Download Flyer
Abstract:
We revisit the mathematics that Ramanujan developed in connection with the famous "taxi-cab" number 1729. A study of his writings reveals that he had been studying Euler's diophantine equation a^3+b^3=c^3+d^3. It turns out that Ramanujan's work anticipated deep structures and phenomena which have become fundamental objects in arithmetic geometry and number theory. We find that he discovered a K3 surface with Picard number 18, one which can be used to obtain infinitely many cubic twists over Q with rank >= 2.
Title: Torsion in Odd Degree
Seminar: Algebra
Speaker: Abbey Bourdon of University of Georgia
Contact: David Zureick-Brown, dzb@mathcs.emory.edu
Date: 2015-12-01 at 4:00PM
Venue: W304
Download Flyer
Abstract:
Let E be an elliptic curve defined over a number field F. It is a classical theorem of Mordell and Weil that the collection of points of E with coordinates in F form a finitely generated abelian group. We seek to understand the subgroup of points with finite order. In particular, given a positive integer d, we would like to know precisely which abelian groups arise as the torsion subgroup of an elliptic curve defined over a number field of degree d. I will discuss recent progress on this problem for the special class of elliptic curves with complex multiplication (CM). In particular, if d is odd, we now have a complete classification of the groups that arise as the torsion subgroup of a CM elliptic curve defined over a number field of degree d. This is joint work with Paul Pollack.