Seminars and Colloquia by Series

Structure-preserving numerical integration or ordinary and partial differential equations

Series
Applied and Computational Mathematics Seminar
Time
Monday, December 1, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Raffaele D'Ambrosio – GA Tech
It is the purpose of this talk to analyze the behaviour of multi-value numerical methods acting as structure-preserving integrators for the numerical solution of ordinary and partial differential equations (PDEs), with special emphasys to Hamiltonian problems and reaction-diffusion PDEs. As regards Hamiltonian problems, we provide a rigorous long-term error analyis obtained by means of backward error analysis arguments, leading to sharp estimates for the parasitic solution components and for the error in the Hamiltonian. As regards PDEs, we consider structure-preservation properties in the numerical solution of oscillatory problems based on reaction-diffusion equations, typically modelling oscillatory biological systems, whose solutions oscillate both in space and in time. Special purpose numerical methods able to accurately retain the oscillatory behaviour are presented.

Homology three-spheres and surgery obstructions

Series
Geometry Topology Seminar
Time
Monday, December 1, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Tye Lidman – University of Texas, Austin
The Lickorish-Wallace theorem states that every closed, connected, orientable three-manifold can be expressed as surgery on a link in the three-sphere (i.e., remove a neighborhood of a disjoint union of embedded $S^1$'s from $S^3$ and re-glue). It is natural to ask which three-manifolds can be obtained by surgery on a single knot in the three-sphere. We discuss a new way to obstruct integer homology spheres from being surgery on a knot and give some examples. This is joint work with Jennifer Hom and Cagri Karakurt.

Alexander's Theorem

Series
Geometry Topology Student Seminar
Time
Wednesday, November 26, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Eric Sabo – Georgia Institute of Technology –

Please Note: This is a project for Prof. Margalit's course on Low-dimensional Topology and Hyperbolic Geometry.

I will present a modern proof of Alexander's Theorem using Morse Theory and surgery.

Some Classic Puzzles of Martin Gardner, The Best Friend Mathematics Ever Had

Series
Other Talks
Time
Tuesday, November 25, 2014 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Colm Mulcahy – Spelman College

Please Note: Colm Mulcahy is a professor of mathematics at Spelman College, in Atlanta, where he has taught since 1988. He's currently on leave in the DC area. Over the last decade, he has been at the forefront of publishing new mathemagical principles and effects for cards, particularly in his long-running bi-monthly Card Colm for the MAA. Some of his puzzles have been featured in the New York Times. His book Mathematical Card Magic: Fifty-Two New Effects was published by AK Peters/CRC Press in 2013. Colm is a recipient of MAA's Allendoerfer Award for excellence in expository writing, for an article on image compression using wavelets.

Martin Gardner was best known for his 300 "Mathematical Games" columns in Scientific American, in which he introduced thousands of budding mathematicians to topics such as RSA cryptography, fractals, Penrose tiles and Conway's game of Life, as well as elegant puzzles which still lead to "Aha!" moments today. In his centennial year we'll survey some of what he achieved and in particular the puzzle legacy he leaves behind.

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.

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