Seminars and Colloquia by Series

Cubic instability in Landau-de Gennes energy for nematic liquid crystals

Series
PDE Seminar
Time
Tuesday, April 9, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xu, Xiang – Carnegie Mellon University
In the Landau-de Gennes theory to describe nematic liquid crystals, there exists a cubic term in the elastic energy, which is unusual but is used to recover the corresponding part of the classical Oseen-Frank energy. And the cost is that with its appearance the current elastic energy becomes unbounded from below. One way to deal with this unboundedness problem is to replace the bulk potential defined as in with a potential that is finite if and only if $Q$ is physical such that its eigenvalues are between -1/3 and 2/3. The main aim of our talk is to understand what can be preserved out of the physical relevance of the energy if one does not use a somewhat ad-hoc potential, but keeps the more common potential. In this case one cannot expect to obtain anything meaningful in a static theory, but one can attempt to see what a dynamical theory can predict.

ARC Theory Day

Series
Other Talks
Time
Tuesday, April 9, 2013 - 09:00 for 8 hours (full day)
Location
Klaus 1116
Speaker
ARC Theory Day – Algorithms and Randomness Center, Georgia Tech
Algorithms and Randomness Center (ARC) Theory Day is an annual event that features hour-long lectures focusing on recent innovative results in theoretical computer science, spanning a wide array of topics several of which are inspired by practical problems. See the complete list of titles and times of talks.

Geometric perspectives on phylogenetics

Series
Algebra Seminar
Time
Monday, April 8, 2013 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Seth Sullivant – North Carolina State University
I will discuss two problems in phylogenetics where a geometric perspective provides substantial insight. The first is the identifiability problem for phylogenetic mixture models, where the main problem is to determine which circumstances make it possible to recover the model parameters (e.g. the tree) from data. Here tools from algebraic geometry prove useful for deriving the current best results on the identifiability of these models. The second problem concerns the performance of distance-based phylogenetic algorithms, which take approximations to distances between species and attempt to reconstruct a tree. A classical result of Atteson gives guarantees on the reconstruction, if the data is not too far from a tree metric, all of whose edge lengths are bounded away from zero. But what happens when the true tree metric is very near a polytomy? Polyhedral geometry provides tools for addressing this question with some surprising answers.

Ferromagnetic crystals and the destruction of minimal foliations

Series
CDSNS Colloquium
Time
Monday, April 8, 2013 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bob W. Rink – Vrije Universiteit Amsterdam
A classical result of Aubry and Mather states that Hamiltonian twist maps have orbits of all rotation numbers. Analogously, one can show that certain ferromagnetic crystal models admit ground states of every possible mean lattice spacing. In this talk, I will show that these ground states generically form Cantor sets, if their mean lattice spacing is an irrational number that is easy to approximate by rational numbers. This is joint work with Blaz Mramor.

Rota's conjecture, the missing axiom, and the tropical Laplacian

Series
Algebra Seminar
Time
Monday, April 8, 2013 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
June Huh – University of Michigan
Rota's conjecture predicts that the coefficients of the characteristic polynomial of a matroid form a log-concave sequence. I will talk about Rota's conjecture and several related topics: the proof of the conjecture for representable matroids, a relation to the missing axiom, and a search for a new discrete Riemannian geometry based on the tropical Laplacian. This is an ongoing joint effort with Eric Katz.

ARC Distinguished Lecture - Algorithmic Pricing

Series
Other Talks
Time
Monday, April 8, 2013 - 15:00 for 1 hour (actually 50 minutes)
Location
Klaus 1116
Speaker
Avrim Blum – Carnegie Mellon University
Pricing and allocating goods to buyers with complex preferences in order to maximize some desired objective (e.g., social welfare or profit) is a central problem in Algorithmic Mechanism Design. In this talk I will discuss some particularly simple algorithms that are able to achieve surprisingly strong guarantees for a range of problems of this type. As one example, for the problem of pricing resources, modeled as goods having an increasing marginal extraction cost to the seller, a simple approach of pricing the i-th unit of each good at a value equal to the anticipated extraction cost of the 2i-th unit gives a constant-factor approximation to social welfare for a wide range of cost curves and for arbitrary buyer valuation functions. I will also discuss simple algorithms with good approximation guarantees for revenue, as well as settings having an opposite character to resources, namely having economies of scale or decreasing marginal costs to the seller.

Statistical Mechanics of the Two-Dimensional Coulomb Gas

Series
Math Physics Seminar
Time
Friday, April 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Pierluigi Falco – California State University, Northridge
The lattice, two dimensional, Coulomb gas is the prototypical model of Statistical Mechanics displaying the 'Kosterlitz-Thouless' phase transition. In this seminar I will discuss conjectures, results and works in progress about this model.

Hypergraph Ramsey Problems

Series
Combinatorics Seminar
Time
Friday, April 5, 2013 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dhruv Mubayi – University of Illinois, Chicago
I will survey the major results in graph and hypergraph Ramsey theory and present some recent results on hypergraph Ramsey numbers. This includes a hypergraph generalization of the graph Ramsey number R(3,t) proved recently with Kostochka and Verstraete. If time permits some proofs will be presented.

Integral homology of hyperbolic three--manifolds

Series
Geometry Topology Seminar
Time
Friday, April 5, 2013 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jean Raimbault – Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie
It is a natural question to ask whether one can deduce topological properties of a finite--volume three--manifold from its Riemannian invariants such as volume and systole. In all generality this is impossible, for example a given manifold has sequences of finite covers with either linear or sub-linear growth. However under a geometric assumption, which is satisfied for example by some naturally defined sequences of arithmetic manifolds, one can prove results on the asymptotics of the first integral homology. I will try to explain these results in the compact case (this is part of a joint work with M. Abert, N. Bergeron, I. Biringer, T. Gelander, N. Nikolov and I. Samet) and time permitting I will discuss their extension to manifolds with cusps such as hyperbolic knot complements.

Tutorial: Information-based complexity of convex optimization

Series
ACO Student Seminar
Time
Friday, April 5, 2013 - 13:05 for 1 hour (actually 50 minutes)
Location
ISyE Executive classroom
Speaker
Cristobal Guzman – ISyE, Georgia Tech –
Information-based complexity is an alternative to Turing complexity that is well-suited for understanding a broad class of convex optimization algorithms. The groundbreaking work of Nemirovski and Yudin provided the basis of the theory, establishing tight lower bounds on the running time of first-order methods in a number of settings. There has been a recent interest on these classical techniques, because of exciting new applications on Machine Learning, Signal Processing, Stochastic Programming, among others. In this talk, we will introduce the rudiments of the theory, some examples, and open problems. Based on joint work with Gábor Braun and Sebastian Pokutta.

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