Seminars and Colloquia by Series

Everywhere differentiability of viscosity solutions to a class of Aronsson's equations

Series
PDE Seminar
Time
Tuesday, November 25, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Changyou Wang – Purdue University
For a $C^{1,1}$-uniformly elliptic matrix $A$, let $H(x,p)=$ be the corresponding Hamiltonian function. Consider the Aronsson equation associated with $H$: $$(H(x,Du))x H_p(x,Du)=0.$$ In this talk, I will indicate everywhere differentiability of any viscosity solution of the above Aronsson's equation. This extends an important theorem by Evans and Smart on the infinity harmonic functions (i.e. $A$ is the identity matrix).

Group actions on spanning trees

Series
Combinatorics Seminar
Time
Tuesday, November 25, 2014 - 13:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Matt Baker – Georgia Tech
The Jacobian group Jac(G) of a finite graph G is a finite abelian group whose cardinality is the number of spanning trees of G. It is natural to wonder whether there is a canonical simply transitive action of Jac(G) on the set of spanning trees which "explains" this numerical coincidence. Surprisingly, this turns out to be related to topological embeddings: we will explain a certain precise sense in which the answer is yes if and only if G is planar. We will also explain how tropical geometry sheds an interesting new light on this picture.

Quantum Entanglement Rates

Series
Job Candidate Talk
Time
Tuesday, November 25, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dr Anna Vershynina – Institute for quantum information, RWTH University Aachen, Germany –

Please Note: Anna Vershynina is a job candidate. She is a Mathematical Physicist working on the rigorous mathematical theory of N-body problem and its relation with quantum information.

Entanglement is one of the crucial phenomena in quantum theory. The existence of entanglement between two parties allows for notorious protocols, like quantum teleportation and super dense coding. Finding a running time for many quantum algorithms depends on how fast a system can generate entanglement. This raises the following question: given some Hamiltonian and dissipative interactions between two or more subsystems, what is the maximal rate at which an ancilla-assisted entanglement can be generated in time. I will review a recent progress on bounding the entangling rate in a closed bipartite system. Then I will generalize the problem first to open system and then to a higher multipartite system, presenting the most recent results in both cases.

Birth & Future of Multi-scale Modeling of Macromolecules

Series
Other Talks
Time
Monday, November 24, 2014 - 16:30 for 2.5 hours
Location
GT Student Center Ballroom
Speaker
2013 Nobel Laureate Michael Levitt – Stanford University

Please Note: Biography: Michael Levitt is an American-British-Israeli biophysicist and professor of structural biology in the Stanford University School of Medicine and a winner of the 2013 Nobel Prize in Chemistry. Born in South Africa in 1947, Levitt earned his Bachelor of Science in Physics from Kings College London and his Ph.D. in biophysics from Cambridge University. His research involves multi-scale approaches to molecular modeling: Coarse-grained models that merge atoms to allow folding simulation and hybrid models that combine classical and quantum mechanics to explain how enzymes works by electrostatic strain. Levitt's diverse interests have included RNA and DNA modeling, protein folding simulation, classification of protein folds and protein geometry, antibody modeling, x-ray refinement, antibody humanization, side-chain geometry, torsional normal mode, molecular dynamics in solution, secondary structure prediction, aromatic hydrogen bonds, structure databases, and mass spectrometry. His Stanford research team currently works on protein evolution, the crystallographic phase problem and Cryo-EM refinement. He is a member of both the Royal Society of London and the U.S. National Academy of Science. Levitt also remains an active computer programmer--"a craft skill of which I am particularly proud," he says.

The development multiscale models for complex chemical systems began in 1967 with publications by Warshel and Levitt recently recognized by the 2013 Nobel Committee for Chemistry. The simplifications used then at the dawn of the age of computational structural biology were mandated by computers that were almost a billion times less cost-effective than those we use today. These same multiscale models have become increasingly popular in application that range from simulation of atomic protein motion, to protein folding and explanation of enzyme catalysis. In this talk I describe the origins of computational structural biology and then go on to show some of the most exciting current and future applications. Please RSVP. Reception begins at 4:30PM; lecture starts at 5:00PM.

Nonnegative curvature and pseudoisotopies

Series
Geometry Topology Seminar
Time
Monday, November 24, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Igor Belegradek – Georgia Tech
I will sketch how to detect nontrivial higher homotopy groups of the space of complete nonnegatively curved metrics on an open manifold.

Quadratic points on hyperelliptic curves

Series
Algebra Seminar
Time
Friday, November 21, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Park – McGill University
Using the ideas of Poonen and Stoll, we develop a modified version of Chabauty's method, which shows that a positive proportion of hyperelliptic curves have as few quadratic points as possible.

Embeddings of manifolds and contact manifolds VI

Series
Geometry Topology Working Seminar
Time
Friday, November 21, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech
This is the sixth (and last) of several talks discussing embeddings of manifolds. I will discuss some general results for smooth manifolds, but focus on embeddings of contact manifolds into other contact manifolds. Particular attention will be paid to embeddings of contact 3-manifolds in contact 5-manifolds. I will discuss two approaches to this last problem that are being developed jointly with Yanki Lekili.

Singularity formation in Compressible Euler equations (Part IV)

Series
PDE Working Seminar
Time
Thursday, November 20, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Ronghua Pan – GeorgiaTech –
Compressible Euler equations describe the motion of compressible inviscid fluid. Physically, it states the basic conservation laws of mass, momentum, and energy. As one of the most important examples of nonlinear hyperbolic conservation laws, it is well-known that singularity will form in the solutions of Compressible Euler equations even with small smooth initial data. This talk will discuss some classical results in this direction, including some most recent results for the problem with large initial data.

Effective Chabauty for symmetric powers of curves

Series
Algebra Seminar
Time
Wednesday, November 19, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Park – McGill University
Faltings' theorem states that curves of genus g> 1 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the number of rational points, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed that Chabauty's method, which works when the Mordell-Weil rank of the Jacobian of the curve is smaller than g, can be used to give a good effective bound on the number of rational points of curves of genus g > 1. We draw ideas from nonarchimedean geometry and tropical geometry to show that we can also give an effective bound on the number of rational points outside of the special set of the d-th symmetric power of X, where X is a curve of genus g > d, when the Mordell-Weil rank of the Jacobian of the curve is at most g-d.

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