All Seminars

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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
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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
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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
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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
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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
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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.
Title: Analysis of Monge-Ampere functions
Seminar: Analysis and Differential Geometry
Speaker: Joseph Fu of University of Georgia
Contact: Vladmir Oliker, oliker@mathcs.emory.edu
Date: 2015-11-24 at 4:00PM
Venue: W301
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Abstract:
The notion of Monge-Ampere (MA) function, introduced by the speaker around 1989 and subsequently generalized by R. Jerrard around 2005, relaxes the strong positivity properties enjoyed by convex functions while preserving the integrality of their derivatives. For example, just as for a convex function there is a natural notion of the Hessian determinant measure for any MA function, with the added flexibility that in the MA case this measure may be signed. In this talk we will give the basic definitions and discuss the main properties and central open questions of this class.
Title: Control of oscillators, temporal homogenization, and energy harvest by super-parametric resonance
Seminar: Numerical Analysis and Scientific Computing
Speaker: Molei Tao of Georgia Institute of Technology
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2015-11-20 at 1:00PM
Venue: W302
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Abstract:
We show how to control an oscillator by periodically perturbing its stiffness, such that its amplitude follows an arbitrary positive smooth function. This also motivates the design of circuits that harvest energies contained in infinitesimal oscillations of ambient electromagnetic fields. To overcome a key obstacle, which is to compensate the dissipative effects due to finite resistances, we propose a theory that quantifies how small/fast periodic perturbations affect multidimensional systems. This results in the discovery of a mechanism that we call super-parametric resonance, which reduces the resistance threshold needed for energy extraction based on coupling a large number of RLC circuits.
Title: K3 Surfaces, Mock Modular Forms and the Conway Group
Seminar: Algebra and Number Theory
Speaker: John Duncan of Emory University
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-11-17 at 4:00PM
Venue: White Hall 112
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Abstract:
In their famous Monstrous Moonshine paper of 1979, Conway Norton also described an association of modular functions to the automorphism group of the Leech lattice (a.k.a. Conways group). In analogy with the monstrous case, there is a distinguished vertex operator superalgebra that realizes these functions explicitly. More recently, it has come to light that this Conway moonshine module may be used to compute equivariant enumerative invariants of K3 surfaces. Conjecturally, all such invariants can be computed in this way. The construction attaches explicitly computable mock modular forms to automorphisms of K3 surfaces.
Title: Local-to-global principle for rational points on conic and quadric bundles over curves
Seminar: Algebra and Number Theory
Speaker: Alexei Skorobogatov of Imperial College London
Contact: Michael H. Mertens, michael.mertens@emory.edu
Date: 2015-11-17 at 5:15PM
Venue: White Hall 112
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Abstract:
One expects the Brauer-Manin obstruction to control rational points on 1-parameter families of conics and quadrics over a number field when the base curve has genus 0. Results in this direction have recently been obtained as a consequence of progress in analytic number theory. On the other hand, it is easy to construct a family of 2-dimensional quadrics over a curve with just one rational point over Q, which is a counterexample to the Hasse principle not detected by the etale Brauer-Manin obstruction. Conic bundles with similar properties exist over real quadratic fields, though most certainly not over Q.
Title: On Large Scale Inverse Problems that Cannot be Solved
Seminar: Numerical Analysis and Scientific Computing
Speaker: Eldad Haber of The University of British Columbia
Contact: Lars Ruthotto, lruthotto@emory.edu
Date: 2015-11-13 at 1:00PM
Venue: W302
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Abstract:
In recent years data collection systems have improved and we are now able to collect large volume of data over vast regions in space. This lead to large scale inverse problems that involve with multiple scales and many data. To invert this data sets, we must rethink our numerical treatment of the problems starting from our discretization, to the optimization technique to be used and the efficient way we can parallelize these problems. In this talk we introduce a new multi-scale asynchronous method for the treatment of such data and apply it to airborne Electromagnetic data.