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Mathematics Colloquium Calendar

Mathematics Colloquium: Xavier Bresson (University of Lausanne), Total Variation Data Analysis - A Non-linear Spectral Framework for Machine Learning Feb 13, 2014 from 01:00 PM to 01:50 PM — NAC 6113,

Mathematics Colloquium: Shirshendu Chatterjee (NYU), Stochastic Spacial Models for some Naturally Occurring Phenomena Feb 18, 2014 from 01:00 PM to 02:00 PM — NAC 6113,

Mathematics Colloquium: Sevak Mkrtchyan (Carnegie Mellon University), The dimer model on the hexagonal lattice Feb 25, 2014 from 01:00 PM to 01:50 PM — TBA,

Mathematics Colloquium: Hau-tieng Wu (Stanford University), Alternating Projection, Ptychography and High Dimensional Phase Retrieval Feb 26, 2014 from 01:00 PM to 01:50 PM — TBA,

Math Colloquium: Alex Lubotzky, "High dimensional expanders and Ramanujan complexes" Sep 04, 2014 from 01:00 PM to 01:55 PM — NAC 6/113,

Mathematics Colloquium: Marian Gidea (Institute for Advanced Study), "How to increase energy with small effort" Feb 07, 2013 from 01:00 PM to 01:50 PM — NA 6113,

Abstract: We will start with a striking result that a geodesic flow on a manifold with a Riemannian (Finsler, Lorenz) metric, perturbed by an external, time-dependent potential, typically has trajectories whose energy grows to infinity. Then we will discuss some general results on instability in Hamiltonian systems; the systems that we consider consist of coupling of several subsystems, and we show how to preferentially increase the energy of one’s choice of subsystem. Our methods are constructive and can be applied to explicit models. We will also discuss some applications of our methods to various disciplines.

Mathematics Colloquium, Khalid Bou-Rabee , U Michigan, "How well approximated is a group by its finite quotients?" Feb 04, 2013 from 01:00 PM to 01:50 PM — NA 6113,

Abstract. We present a systematic approach for tackling the question in the title by introducing some numerical invariants that quantify residual finiteness. We will work out a number of examples and exhibit phenomena relating group theoretic properties with certain growths of this invariant. This talk covers joint work with Tasho Kaletha and Ben McReynolds.

Mathematics Colloquium: Kamiar Rahnama Rad (Columbia University), "High dimensional information processing with limited resources in neural systems" Feb 05, 2013 from 01:00 PM to 01:50 PM — NA 6113,

Abstract: As is the case in many information processing systems, in the nervous system information processing is performed by multiple neuronal networks each having access to different types and amounts of information. To understand information processing in the brain, we should thus study learning approaches that are based on computationally efficient information sharing methods. This is the focus of this talk. The first part of the talk will focus on a network of observers making local observations concerning an unknown vector. Each node faces a local identification problem, in the sense that it cannot consistently estimate the parameter in isolation. Employing a novel local message passing algorithm, I will show that despite local identification problems, local estimates can be as efficient as any ideal global estimator. In the second part of the talk, I will discuss optimal decoding, information rates and dimensionality reduction of high dimensional spatio-temporally correlated spiking activities. In particular, I will show that neural populations with strong history-dependent (non-Poisson) effects carry exactly the same information as do simpler equivalent populations of non-interacting Poisson neurons with matched firing rates. Finally, I will present a scalable and robust method for extracting as much information as possible from the simultaneously recorded activity of tens of thousands of neurons. The methodological innovation of our work is to use a regularizer that is robust to occasional discontinuities, and nevertheless if there is enough evidence in the data, enforces similarity between nearby neurons, all in an adaptive fashion.

Mathematics Colloquium: Julie Rowlett (University of Goettingen), "Geometric Analysis from Drums to Dynamics" Feb 11, 2013 from 01:00 PM to 02:00 PM — Artino Lab (NAC 1/511),

Abstract: Have you ever wondered why, when a rock guitarist plays high notes in a solo, he grips the strings down low on the guitar? Geometry affects physical properties, like sound, which can be described using analysis in general, and spectral theory in particular. We will begin with motivating examples and proceed to investigate M. Kac's question, ``Can one hear the shape of a drum?" Spectral theory can be used not only to describe sound travel but also to describe the energy states of quantum particles. We will next explore relationships between the spectrum and Hamiltonian dynamics on some complete, negatively curved manifolds. In conclusion, I will discuss further directions and applications of geometric analysis.

Mathematics Colloquium: Liz Vivas (Purdue University), "Dynamics of homomorphic self-maps near a fixed point" Feb 14, 2013 from 01:00 PM to 02:00 PM — NA 6113,

Math Colloquium: Partha Sarathi Dey (NYU), Energy Landscape for `large average' Gaussian submatrices. Feb 19, 2013 from 01:00 PM to 01:50 PM — NA 6113,

Math Colloquium: Alexandra Chronopoulou (UCSB), Statistical Inference for fractional SDEs and applications Feb 21, 2013 from 01:00 PM to 01:50 PM — NA 6113,

Mathematics Colloquium, Gautam Chinta, CCNY, "Cubic forms and cubic rings" Sep 27, 2012 from 01:00 PM to 02:00 PM — NAC 6/113,

Mathematics Colloquium, Anders Karlsson, University of Geneva, "Noncommuting random products" Oct 04, 2012 from 01:00 PM to 02:00 PM — United States,

In a seminal paper from 1963 Furstenberg inquired to what extent the law of large numbers in probability extends to a noncommutative setting when the random variables take values in a group more general than the additive reals. Questions related to this have been studied extensively over the years. Applications can notably be found in the theory of smooth dynamical systems, in difference equations with random coefficients and in Margulis' proof of superrigidity and arithmeticity for higher rank lattices in Lie groups. I will present a relatively recent and general such noncommutative ergodic theorem obtained in a joint work with F. Ledrappier. I will outline a few of its applications, for example to Brownian motion and harmonic functions on Riemannian manifolds, or to an extension of the spectral theorem for surface homeomorphisms due to Thurston.

Mathematics Colloquium, Conchita Martínez-Pérez, Universidad de Zaragoza, Spain, "Euler classes of virtually solvable groups of type FP-infinity" Oct 11, 2012 from 01:00 PM to 02:00 PM — NAC 6/113,

The Euler class of a group admitting a cocompact classifying space for proper actions was first defined by Lück and is closely related to several Euler characteristics for groups. We show how to use posets of finite subgroups to obtain some formulas for the Euler class of a virtually solvable group of type FP_\infty.

Mathematics Colloquium, Marian Gidea, Institute for Advanced Study, Topological methods in Hamiltonian instability Oct 18, 2012 01:00 PM — NAC 6/113,

A Hamiltonian system represents a model for the evolution of a physical system. If the system is integrable, then all solutions are rather explicit. A typical Hamiltonian system, however, is non-integrable, exhibiting instability. A paradigm for Hamiltonian instability is the 'Arnold diffusion problem', asserting that a generic, integrable Hamiltonian system subjected to a small perturbation has solutions that travel 'wildly and arbitrarily far' in the phase space. We will present a topological approach to the Hamiltonian instability problem. We will apply this to detect diffusing orbits under rather explicit conditions on the unperturbed system and on the perturbation. The topological method is constructive and can be implemented in numerical experiments. We will show some applications to space mission design.

Mathematics Colloquium, Fernando Schwartz, U Tennessee, "Geometric Inequalities for Hypersurfaces" Dec 06, 2012 from 01:00 PM to 02:00 PM — United States,

Abstract: I will begin this talk by recalling the classic inequalities of Alexandrov-Fenchel and Polya-Szego for convex surfaces of 3-dimensional Euclidean space. Then, I will present my joint work with Freire, which generalizes the inequalities -with rigidity- to both a larger class of hypersurfaces and to arbitrary dimensions. I will conclude by mentioning some applications of the results, including an inequality for black holes.

(Canceled) Math Colloquium: Martin Schmoll: Orbits on infinite surfaces stabilized by pseudo-Anosovs May 17, 2011 from 01:00 PM to 01:50 PM — NAC 6-113,

Cancelled: See note below. Math Colloquium talk by Martin Schmoll of Clemson University.

Math Colloquium: Arthur Szlam, "Low rank and block low rank matrix approximation" May 03, 2011 from 01:00 PM to 01:50 PM — NAC 1/511E,

Arthur Szlam (Courant Institute)

Math Colloquium: Stuart Margolis: On Some Monoids Associated to Coxeter Groups Sep 20, 2011 from 01:00 PM to 02:00 PM — NAC 6-113,

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