Seminars and Colloquia by Series

Thursday, March 3, 2016 - 16:05 , Location: Skiles 005 , Peter Trapa , University of Utah , Organizer:
Unitary representations of Lie groups appear in many guises in mathematics: in harmonic analysis (as generalizations of classical Fourier analysis); in number theory (as spaces of modular and automorphic forms); in quantum mechanics (as "quantizations" of classical mechanical systems); and in many other places. They have been the subject of intense study for decades, but their classification has only  recently emerged. Perhaps surprisingly, the classification has inspired connections with interesting geometric objects (equivariant mixed Hodge modules on flag varieties). These connections have made it possible to extend the classification scheme to other related settings. The purpose of this talk is to explain a little bit about the history and motivation behind the study of unitary representations and offer a few hints about the algebraic and geometric ideas which enter into their study. This is based on joint work with Adams, van Leeuwen, and Vogan.
Thursday, March 3, 2016 - 11:00 , Location: Skiles 006 , Daniel Fiorilli , University of Ottawa , daniel.fiorilli@uottawa.ca , Organizer: Michael Damron
While the fields named in the title seem unrelated, there is a strong link between them. This amazing connection came to life during a meeting between Freeman Dyson and Hugh Montgomery at the Institute for Advanced Study. Random matrices are now known to predict many number theoretical statistics, such as moments, low-lying zeros and correlations between zeros. The goal of this talk is to discuss this connection, focusing on number theory. We will cover both basic facts about the zeta functions and recent developments in this active area of research.
Monday, February 29, 2016 - 16:05 , Location: Skiles 005 , Hongkai Zhao , University of California, Irvine , Organizer: Haomin Zhou
One of the simplest and most natural ways of representing geometry and information in three and higher dimensions is using point clouds, such as scanned 3D points for shape modeling and feature vectors viewed as points embedded in high dimensions for general data analysis. Geometric understanding and analysis of point cloud data poses many challenges since they are unstructured, for which a global mesh or parametrization is difficult if not impossible to obtain in practice. Moreover, the embedding is highly non-unique due to rigid and non-rigid transformations. In this talk, I will present some of our recent work on geometric understanding and analysis of point cloud data. I will first discuss a multi-scale method for non-rigid point cloud registration based on the Laplace-Beltrami eigenmap and optimal transport. The registration is defined in distribution sense which provides both generality and flexibility. If time permits I will also discuss solving geometric partial differential equations directly on point clouds and show how it can be used to “connect the dots” to extract intrinsic geometric information for the underlying manifold.
Thursday, February 25, 2016 - 11:05 , Location: Skiles 006 , Stefan Siegmund , TU Dresden , stefan.siegmund@tu-dresden.de , Organizer: Michael Damron
From theoretical to applied, we present curiosity driven research which goes beyond classical dynamical systems theory and (i) extend the notion of chaos to actions of topological semigroups, (ii) model how the human bone renews, (iii) study transient dynamics as it occurs e.g. in oceanography, (iv) understand how to protect houses from hurricane damage. The talk introduces concepts from topological dynamics, mathematical biology, entropy theory and mechanics.
Monday, February 22, 2016 - 16:00 , Location: Skiles 005 , Michael Loss , School of Mathematics, Georgia Tech , Organizer:
The Caffarelli-Kohn-Nirenberg inequalities form a two parameter family of inequalities that interpolate between Sobolev's inequality and Hardy's inequality. The functional whose minimization yields the sharp constant is invariant under rotations. It has been known for some time that there is a region in parameter space where the optimizers for the sharp constant are {\it not} radial. In this talk I explain this and related problems andindicate a proof that, in the remaining parameter region, the optimizers are in fact radial. The novelty is the use of a flow that decreases the functional unless the function is a radial optimizer. This is joint work with Jean Dolbeault and Maria Esteban.
Thursday, February 11, 2016 - 16:05 , Location: Skiles 005 , Rachel Kuske , University of British Columbia , Organizer: Christine Heitsch
There have been many recent advances for analyzing the complex deterministic behavior of systems with discontinuous dynamics. With the identification of new types of nonlinear phenomena exploding in this realm, one gets the feeling that almost anything can happen. There are many open questions about noise-driven and noise-sensitive phenomena in the non-smooth context, including the observation that noise can facilitate or select "regular" dynamics, thus clarifying the picture within the seemingly endless sea of possibilities. Familiar concepts from smooth systems such as escapes, resonances, and bifurcations appear in unexpected forms, and we gain intuition from seemingly unrelated canonical models of biophysics, mechanics, finance, and climate dynamics. The appropriate strategy is often not immediately obvious from the area of application or model type, requiring an integration of multiple scales techniques, probabilistic models, and nonlinear methods.
Tuesday, February 9, 2016 - 15:30 , Location: Skiles 005 , Patrick Gerard , Université Paris-Sud , patrick.gerard@math.u-psud.fr , Organizer: Michael Damron
In the world of Hamiltonian partial differential equations, complete integrability is often associated to rare and peaceful dynamics, while wave turbulence rather refers to more chaotic dynamics. In this talk I will first try to give an idea of these different notions. Then I will  discuss the example of the cubic Szegö equation, a nonlinear wave toy model which surprisingly displays both properties. The key is a Lax pair structure involving Hankel operators from classical analysis, leading to the inversion of large ill-conditioned matrices. .
Monday, February 8, 2016 - 16:00 , Location: Skiles 005 , Jesus De Loera , University of California, Davis , Organizer: Greg Blekherman
Convex analysis and geometry are tools fundamental to the foundations of several applied areas (e.g., optimization, control theory, probability and statistics),  but at the same time convexity intersects in lovely ways with topics considered pure (e.g., algebraic geometry, representation theory and of course number theory). For several years I have been interested interested on how convexity relates to lattices and discrete subsets of Euclidean space. This is part of mathematics  H. Minkowski named in 1910 "Geometrie der Zahlen''.  In this talk I will use two well-known results, Caratheodory's & Helly's theorems, to explain my most recent work on lattice points on convex sets. The talk is for everyone! It is designed for non-experts and grad students should understand the key ideas. All new theorems are joint work with subsets of the following mathematicians I. Aliev, C. O'Neill, R. La Haye, D. Rolnick, and P. Soberon.
Thursday, February 4, 2016 - 11:00 , Location: Skiles 006 , Prof. Dr. Adilson E. Motter , Northwestern University , motter@northwestern.edu , Organizer: Molei Tao
The recent interest in network modeling has been largely driven by the prospect that network optimization will help us understand the workings of evolution in natural systems and the principles of efficient design in engineered systems. In this presentation, I will reflect on unanticipated properties observed in three classes of network optimization problems. First, I will discuss implications of optimization for the metabolic activity of living cells and its role in giving rise to the recently discovered phenomenon of synthetic rescues. I will then comment on the problem of controlling network dynamics and show that theoretical results on optimizing the number of driver nodes often only offer a conservative lower bound to the number actually needed in practice. Finally, I will discuss the sensitive dependence of network dynamics on network structure that emerges in the optimization of network topology for dynamical processes governed by eigenvalue spectra, such as synchronization and consensus processes. It follows that optimization is a double-edged sword for which desired and adverse effects can be exacerbated in network systems due to the high dimensionality of their phase spaces.
Thursday, January 28, 2016 - 11:05 , Location: Skiles 006 , Leonid Bunimovich , Georgia Institute of Technology , leonid.bunimovich@math.gatech.edu , Organizer: Michael Damron
Hepatitis C virus (HCV) has the propensity to cause chronic infection. HCV affects an estimated 170 million people worldwide. Immune escape by continuous genetic diversification is commonly described using a metaphor of "arm race" between virus and host. We developed a mathematical model that explained all clinical observations which could not be explained by the "arm race theory". The model applied to network of cross-immunoreactivity suggests antigenic cooperation as a mechanism of mitigating the immune pressure on HCV variants. Cross-immunoreactivity was observed for dengue, influenza, etc.   Therefore antigenic cooperation is a new target for therapeutic- and vaccine- development strategies.  Joint work with P.Skums and Yu. Khudyakov (CDC).  Our model is in a sense simpler than old one. In the speaker's opinion it is a good example to discuss what Math./Theor. Biology is and what it should be. Such (short) discussion is expected. NO KNOWLEDGE of Biology is expected to understand this talk.

Pages