Seminars and Colloquia Schedule

Discrete Mathematical Biology Working Seminar

Series
Other Talks
Time
Monday, February 27, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Shel Swenson – Georgia Tech
The paper "Abstract shapes of RNA" (2004) by Giegerich, Voss, and Rehmsmeier will be discussed.

Transitivity of nilpotent extensions of hyperbolic systems

Series
CDSNS Colloquium
Time
Monday, February 27, 2012 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Andrew Torok – Univ. of Houston
Consider a hyperbolic basic set of a smooth diffeomorphism. We are interested in the transitivity of Holder skew-extensions with fiber a non-compact connected Lie group. In the case of compact fibers, the transitive extensions contain an open and dense set. For the non-compact case, we conjectured that this is still true within the set of extensions that avoid the obvious obstructions to transitivity. Within this class of cocycles, we proved generic transitivity for extensions with fiber the special Euclidean group SE(2n+1) (the case SE(2n) was known earlier), general Euclidean-type groups, and some nilpotent groups. We will discuss the "correct" result for extensions by the Heisenberg group: if the induced extension into its abelinization is transitive, then so is the original extension. Based on earlier results, this implies the conjecture for Heisenberg groups. The results for nilpotent groups involve questions about Diophantine approximations. This is joint work with Ian Melbourne and Viorel Nitica.

Nodal count of eigenfunctions as index of instability

Series
Math Physics Seminar
Time
Monday, February 27, 2012 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Gregory Berkolaiko – Texas A&M Univ. –
Zeros of vibrational modes have been fascinating physicists for several centuries. Mathematical study of zeros of eigenfunctions goes back at least to Sturm, who showed that, in dimension d=1, the n-th eigenfunction has n-1 zeros. Courant showed that in higher dimensions only half of this is true, namely zero curves of the n-th eigenfunction of the Laplace operator on a compact domain partition the domain into at most n parts (which are called "nodal domains"). It recently transpired that the difference between this "natural" number n of nodal domains and the actual values can be interpreted as an index of instability of a certain energy functional with respect to suitably chosen perturbations. We will discuss two examples of this phenomenon: (1) stability of the nodal partitions of a domain in R^d with respect to a perturbation of the partition boundaries and (2) stability of a graph eigenvalue with respect to a perturbation by magnetic field. In both cases, the "nodal defect" of the eigenfunction coincides with the Morse index of the energy functional at the corresponding critical point. Based on preprints arXiv:1107.3489 (joint with P.Kuchment and U.Smilansky) and arXiv:1110.5373

On triangulating a square

Series
Geometry Topology Seminar
Time
Monday, February 27, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Aaron Abrams – Emory University
I will discuss the following geometric problem. If you are given an abstract 2-dimensional simplicial complex that is homeomorphic to a disk, and you want to (piecewise linearly) embed the complex in the plane so that the boundary is a geometric square, then what are the possibilities for the areas of the triangles? It turns out that for any such simplicial complex there is a polynomial relation that must be satisfied by the areas. I will report on joint work with Jamie Pommersheim in which we attempt to understand various features of this polynomial, such as the degree. One thing we do not know, for instance, if this degree is expressible in terms of other known integer invariants of the simplicial complex (or of the underlying planar graph).

Fungal fluid mechanics

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 27, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Marcus Roper – UCLA Mathematics Dept.
Although fungi are the most diverse eukaryotic organisms, we have only a very fragmentary understanding of their success in so many niches or of the processes by which new species emerge and disperse. I will discuss how we are using math modeling and perspectives from physics and fluid mechanics to understand fungal life histories and evolution: #1. A growing filamentous fungi may harbor a diverse population of nuclei. Increasing evidence shows that this internal genetic flexibility is a motor for diversification and virulence, and helps the fungus to utilize nutritionally complex substrates like plant cell walls. I'll show that hydrodynamic mixing of nuclei enables fungi to manage their internal genetic richness. #2. The forcibly launched spores of ascomycete fungi must eject through a boundary layer of nearly still air in order to reach dispersive air flows. Individually ejected microscopic spores are almost immediately brought to rest by fluid drag. However, by coordinating the ejection of thousands or hundreds of thousands of spores fungi, such as the devastating plant pathogen Sclerotinia sclerotiorum are able to create a flow of air that carries spores across the boundary layer and around any intervening obstacles. Moreover the physical organization of the jet compels the diverse genotypes that may be present within the fungus to cooperate to disperse all spores maximally.

The central curve of a linear program

Series
Algebra Seminar
Time
Tuesday, February 28, 2012 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Cynthia Vinzant – University of Michigan
The central curve of a linear program is an algebraic curve specified by a hyperplane arrangement and a cost vector. This curve is the union of the various central paths for minimizing or maximizing the cost function over any region in this hyperplane arrangement. I will discuss the algebraic properties of this curve and its beautiful global geometry, both of which are controlled by the corresponding matroid and hyperplane arrangement.

Stochastic Scalar Conservation Law

Series
PDE Seminar
Time
Tuesday, February 28, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jin Feng – University of Kansas
This talk considers a scalar conservation (balance) law equation with random (martingale measure) source term. A new notion of entropic solution is introduced as the underlying calculus for change of variable needs to be changed into Ito's calculus. This is due to irregularities in the trajectory of particles caused by randomness. In the new notion, entropy production has additional terms. We discuss ways to handle such term so that a uniqueness theory can still be established. Additionally, stochastic generalizations of compensated compactness will be given. This was a joint work with David Nualart. It appeared in Journal of Functional Analysis, Vol 255, Issue 2, 2008, pages 313-373.

Modeling angiogenesis from pathways to tissue

Series
Mathematical Biology Seminar
Time
Wednesday, February 29, 2012 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yi Jiang – GSU –
Angiogenesis, growth of new blood vessels from existing ones, is animportant process in normal development, wound healing, and cancer development.  Presented with increasingly complex biological data and observations, the daunting task is to develop a mathematical model that is useful, i.e. can help to answer important and relevant questions, or to test a hypothesis, and/or to cover a novel mechanism. I will present two cell-based multiscale models focusing on biochemical (vescular endothelial growth factors) and biomechanical (extra-cellular matrix) interactions.  Our models consider intracellular signaling pathways, cell dynamics, cell-cell andcell-environment interactions. I will show that they reproduced someexperimental observations, tested some hypotheses, and generated more hypotheses.

KPZ in equilibrium and directed polymers

Series
Stochastics Seminar
Time
Thursday, March 1, 2012 - 15:05 for 1 hour (actually 50 minutes)
Location
Skyles 006
Speaker
Gregorio Moreno Flores – University of Wisconsin, department of Mathematics
The usual approach to KPZ is to study the scaling limit of particle systems. In this work, we show that the partition function of directed polymers (with a suitable boundary condition) converges, in a certain regime, to the Cole-Hopf solution of the KPZ equation in equilibrium. Coupled with some bounds on the fluctuations of directed polymers, this approach allows us to recover the cube root fluctuation bounds for KPZ in equilibrium. We also discuss some partial results for more general initial conditions.

Game Dynamics and Equilibria

Series
ACO Distinguished Lecture
Time
Thursday, March 1, 2012 - 16:30 for 1 hour (actually 50 minutes)
Location
Klaus 1116
Speaker
Sergiu Hart – Hebrew University of Jerusalem

Reception in the Atrium of the Klaus building at 4PM.

The concept of "strategic equilibrium," where each player's strategy is optimal against those of the other players, was introduced by John Nash in his Ph.D. thesis in 1950. Throughout the years, Nash equilibrium has had a most significant impact in economics and many other areas. However, more than 60 years later, its dynamic foundations - how are equilibria reached in long-term interactions - are still not well established. In this talk we will overview a body of work of the last decade on dynamical systems in multi-player environments. On the one hand, the natural informational restriction that each participant may not know the payoffs and utilities of the other participants - "uncoupledness" - turns out to severely limit the possibilities to converge to Nash equilibria. On the other hand, there are simple adaptive heuristics - such as "regret matching" - that lead in the long run to correlated equilibria, a concept that embodies full rationality. We will also mention connections to behavioral and neurobiological studies, to computer science concepts, and to engineering applications.

Spatial mixing in spin systems

Series
ACO Student Seminar
Time
Friday, March 2, 2012 - 13:00 for 1 hour (actually 50 minutes)
Location
TBA
Speaker
Linji Yang – CoC, Georgia Tech
In this seminar, I will talk about a few recent developments in the random colorings, random weighted independent sets and other 2-spin models on different classes of graphs such as the square lattices and the triangular free graphs. I will focus on the so-called spatial mixing property of these models and discuss about the consequences (e.g., fast mixing of the Markov chains) of the spatial mixing property as well as the techniques of proving it.