FEBRUARY 2011

Discrete Mathematics Seminar

Topic:

Color 6-critical graphs on surfaces

Presenter:

Robin Thomas, Georgia Tech

Date: 

Thursday, February 24, 2011, Time: 2:15 p.m., Location: Fine Hall 224

Abstract:

We give a simple proof of a theorem of Thomassen that for every surface S there are only finitely many 6-critical graphs that embed in S. With a little bit of additional effort we can bound the number of vertices of a 6-critical graph embedded in S by a function that is linear in the genus of S. This is joint work with Luke Postle.

Algebraic Topology Seminar

Topic:

On spaces of homomorphisms and spaces of representations

Presenter:

Fred Cohen, University of Rochester and IAS

Date: 

Thursday, February 24, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

The subject of this talk is the structure of the space of homomorphisms from a group \pi to a Lie group G denoted Hom(\pi,G). The space of representations Hom(\pi,G)/G obtained from the adjoint action of G will be considered. In special cases, these spaces can be assembled into a single space analogous to the classifying space of the group G. Properties of these spaces will be developed. This talk is based on joint work with A. Adem, E. Torres, and J. Gomez.

Princeton University and IAS Number Theory Seminar

Topic:

Whittaker Functions and Demazure Characters

Presenter:

Daniel Bump, Stanford University

Date: 

Thursday, February 24, 2011, Time: 4:30 p.m., Location: Fine Hall 214

Abstract:

It is well-known that there are connections between the representation theory of a reductive p-adic
group and the topology of the flag variety of the Langlands L-group. We will discuss Whittaker functions in this light. The Casselman-Shalika formula shows that the values of the spherical Whittaker function are the same as the characters of irreducible representations of the L-group. The Borel-Weil-Bott theorem identifies these same characters as cohomology groups of line bundles on the flag variety. Generalizing the Borel-Weil-Bott theorem, cohomology groups of line bundles on Schubert varieties are "Demazure characters". We will show how Demazure characters also appear in Iwahori Whittaker functions. This is joint work with Ben Brubaker and Anthony Licata.

Topology Seminar

Topic:

Right-angledness, flag complexes, asphericity

Presenter:

Mike Davis, Ohio State and IAS

Date:

Thursday, February 24, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:

I will discuss three related constructions of spaces and manifolds and then  give necessary and sufficient conditions for the resulting spaces to be aspherical.  The first construction is the polyhedral product functor.  The second construction involves applying the reflection group trick to a "corner of spaces".  The third construction involves pulling back a corner of spaces via a coloring of a simplicial complex.  The two main sources of examples of corners which yield aspherical results are: 1) products of aspherical manifolds with (aspherical) boundary and 2) the Borel-Serre bordification of torsion-free arithmetic groups which are nonuniform lattices.

Differential Geometry and Geometric Analysis Seminar

Topic:

On unique continuation for nonlinear elliptic equations

Presenter:

Luis Silvestre, Chicago

Date: 

Friday, February 25, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

We will discuss the following issue: if two solutions of a nonlinear elliptic equation coincide in a small ball, do they necessarily coincide everywhere? The problem is fairly well understood in the linear setting, but it is open for most interesting nonlinear elliptic equations. We will analyze the difficulties of the problem and prove a result in arguably the simplest case in which one cannot linearize the equation a priori.

Joint Analysis Seminar and PACM Colloquium

Topic:

Invertibility of random matrices and applications

Presenter:

Roman Vershynin, University of Michigan

Date:

Monday, February 28, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Abstract:

Consider an n by n random matrix H with independent entries. As the dimension grows to infinity, how likely is H to be invertible? And what is the typical norm of the inverse? These questions can be traced back to P. Erdos (for matrices with +1,-1 entries) and von Neumann and his collaborators (motivated by the analysis of numerical algorithms). For both matrices with all independent entries and for symmetric random matrices, there was a considerable progress on the invertibility problem in the last few years. The methods come from different areas, including classical random matrix theory, mathematical physics, geometrical functional analysis, and additive combinatorics. A related problem for rectangular random matrices is motivated by statistical applications (covariance estimation). We will discuss recent progress and several conjectures.

MARCH 2011

Algebraic Geometry Seminar

Topic:

TBA

Presenter:

Karen Smith, Univ. of Michigan

Date: 

Tuesday, March 1, 2011, Time: 4:30 p.m., Location: Fine Hall 322

Department Colloquium

Topic:

New theory of hypergeometric functions

Presenter:

Ivan Cherednik, University of North Carolina

Date: 

Wednesday, March 2, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:

The lecture will be devoted to the new vintage in the theory of special functions, a unification of the Bessel, hypergeometric, spherical and Whittaker functions, their p-adic and difference counterparts, and of course the theta-functions (associated with root systems) in one definition. The latter was suggested 13 years ago, but a reasonably complete analytic theory of such "global spherical functions" was created only recently, including the Harish-Chandra asymptotic formula and many more. These global functions generalize the classical q-hypergeometric (basic) series introduce by Heine in 1846, but the new approach is very different even for one variable. Algebraically, the global functions are actually similar to the Bessel functions. For instance, the corresponding Fourier transform is essentially involutive (like for the classical Hankel transform), which is broken in the Harish-Chandra theory and its p-adic counterpart. The construction is based on DAHA, q-deformations of the classical Heisenberg-Weyl algebras. The Lie theory was expected to provide such unification (the Gelfand program) but it did not materialize. The new theory actually begins with "nonsymmetric" global spherical functions (eigenfunctions of first order opertators) and their counterparts everywhere (including "nonsymmetric" Schur functions), which is generally beyond the Lie theory. It clarifies why we need to go "back" to the Heisenberg algebras and their deformations. The case of rank one will be mainly considered; no special knowledge of representation theory is assumed.

Ergodic Theory and Statistical Mechanics Seminar  **Please note change in room number**

Topic:

Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions

Presenter:

Ivan Corwin, Courant Institute, NYU

Date: 

Thursday, March 3, 2011, Time: 2:00 p.m., Location: Fine Hall 801

Abstract:

We consider the solution of the stochastic heat equation with multiplicative noise and delta function initial condition whose logarithm, with appropriate normalizations, is the free energy of the continuum directed polymer, or the solution of the Kardar-Parisi-Zhang equation with narrow wedge initial conditions. We prove explicit formulas for the one-dimensional marginal distributions -- the crossover distributions -- which interpolate between a standard Gaussian distribution (small time) and the GUE Tracy-Widom distribution (large time). The proof is via a rigorous steepest descent analysis of the Tracy-Widom formula for the asymmetric simple exclusion with anti-shock initial data, which is shown to converge to the continuum equations in an appropriate weakly asymmetric limit. The limit also describes the crossover behaviour between the symmetric and asymmetric exclusion processes.

Discrete Mathematics Seminar

Topic:

TBA

Presenter:

Zeev Dvir, Princeton University

Date: 

Thursday, March 3, 2011, Time: 2:15 p.m., Location: Fine Hall 224

Algebraic Topology Seminar

Topic:

The Unstable Chromatic Spectral Sequence

Presenter:

Martin Bendersky, The City University of New York

Date: 

Thursday, March 3, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Princeton University and IAS Number Theory Seminar

Topic:

Periods of quaternionic Shimura varieties

Presenter:

Kartik Prasanna, University of Michigan, Ann Arbor

Date: 

Thursday, March 3, 2011, Time: 4:30 p.m., Location: S-101 at IAS

Abstract:

In the early 80's, Shimura made a precise conjecture relating Petersson inner products of arithmetic automorphic forms on quaternion algebras over totally real fields, up to algebraic factors. This conjecture (which is a consequence of the Tate conjecture on algebraic cycles) was proved a few years later by Michael Harris. In the first half of my talk I will motivate and describe an integral version of Shimura's conjecture i.e. up to p-adic units for a good prime p. In the second half I will describe work in progress (joint with Atsushi Ichino) that makes some progress in understanding this refined conjecture.

Topology Seminar

Topic:

Nondistorted subgroups of Out(F_n), via Lipschitz retraction in spaces of trees (joint work with M. Handel)

Presenter:

Lee Mosher, Rutgers University

Date: 

Thursday, March 3, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:

We prove that various subgroups of Out(F_n) --- the outer automorphism group of a free group of rank n --- such as the stabilizer of the conjugacy class of a rank n-1 free factor, are undistorted in Out(F_n). The method of proof is to show that these subgroups are Lipschitz retracts of the ambient group, in fact we construct these retractions in appropriate spaces of trees on which F_n acts.

Differential Geometry and Geometric Analysis Seminar

Topic:

An Aronsson type approach to extremal quasiconformal mappings

Presenter:

Luca Capogna, University of Arkansas

Date: 

Friday, March 4, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

Quasiconformal mappings $u:\Omega\to \Omega'$  between open domains in $\R^n$,  are $ W^{1,n}$ homeomorphisms whose dilation $K=|du|/ (det du)^1/n$ is in $L^\infty$. A classical problem in geometric function theory consists in finding QC minimizers for the dilation within  a given homotopy class or with prescribed boundary data.  In a joint work with A. Raich we study $C^2$ extremal quasiconformal mappings in space and establish necessary and sufficient conditions for a `localized' form of extremality in the spirit of the work of G. Aronsson on absolutely minimizing Lipschitz extensions. We also prove short time existence for smooth solutions of a gradient flow of QC diffeomorphisms associated to the extremal problem.

Mathematical Physics Seminar **please note special day, time and location**

Topic:

Geometry of quantum response in open systems

Presenter:

Yosi Avron, Technion (Israel)

Date:

Friday, March 4, 2011, Time: 11:00 a.m., Location: A09 Jadwin Hall

Abstract:

I shall describe a theory of adiabatic response for controlled open systems governed by Lindblad evolutions. The theory gives quantum response a geometric interpretation induced from the geometry of Hilbert space projections. For a two level system the metric turns out to be the Fubini-Study metric and the symplectic form the adiabatic curvature. Nice things happen when the metric and symplectic structures are compatible so the space of controls is Kahler. I shall give examples of compatible physical systems. Work based on joint work with Fraas, Graf and Kenneth.

PACM Colloquium

Topic:

Generalized Markov models in population genetics

Presenter:

Joshua Plotkin, University of Pennsylvania

Date:

Monday, March 7, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Abstract:

Population geneticists study the dynamics of alternative genetic types in a replicating population. Most theoretical works rests on a simple Markov chain, called the Wright-Fisher model, to describe how an allele's frequency changes from one generation to the next. We have introduced a broad class of Markov models that share the same mean and variance as the Wright-Fisher model, but may otherwise differ. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We have characterized the behavior of standard population-genetic quantities across this family of generalized models. The generalized population models can produce startling phenomena that differ qualitatively from classical behavior -- such as assured fixation of a new mutant despite the presence of genetic drift. We have derived the forward-time continuum limits of the generalized processes, analogous to Kimura's diffusion limit of the Wright-Fisher process. Finally, we have shown that some of these exotic models are more likely than the Wright-Fisher model itself, given empirical data on genetic variation in Drosophila populations. Joint work with Ricky Der and Charlie Epstein.

Algebraic Geometry Seminar

Topic:

TBA

Presenter:

Kyungyong Lee, U. Conn.

Date:

Tuesday, March 8, 2011, Time: 4:30 p.m., Location: Fine Hall 322

Department Colloquium (joint with ORFE)

Topic:

The spectrum of non-normal random matrices

Presenter:

Alice Guionnet, ENS, Lyon, France

Date: 

Wednesday, March 9, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:

We will discuss the asymptotics of the spectrum of non-normal random matrices with size going to infinity, and in particular the single ring phenomenon observed for unitary invariant models.

Department Colloquium (joint with ORFE) **please note special date, time and location**

Topic:

Topological expansion for random matrices

Presenter:

Alice Guionnet, ENS, Lyon, France

Date: 

Thursday, March 10, 2011, Time: 12:00 p.m., Location: Room 101, Sherrerd (ORFE Bldg.)

Abstract:

It is known till 't Hooft and Brezin-Itzykson-Paris and Zuber that the partition function of random matrices expand formally as a generating function for the enumeration of graphs sorted by their genera. We shall show that this expansion can be turned into an asymptotic expansion in a wide variety of models, including the so-called beta models.

Algebraic Topology Seminar

Topic:

Nonimmersions of real projective spaces and tmf

Presenter:

Don Davis, Lehigh University

Date: 

Thursday, March 10, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

We use the spectrum tmf to obtain new nonimmersion results for many real projective spaces RP^n for n as small as 113. The only new ingredient is some new calculations of tmf-cohomology groups. We present an expanded table of nonimmersion results. We also present several questions about tmf.

Topology Seminar

Topic:

TBA

Presenter:

Matt Hedden, Michigan State

Date: 

Thursday, March 10, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Ergodic Theory and Statistical Mechanics Seminar **please note special day & change in room number**

Topic:

Diffusion in a periodic Lorentz gas with narrow tunnels (P. Balint, N. Chernov, and D. Dolgopyat)

Presenter:

Nikolai Chernov, University of Alabama at Birmingham

Date: 

Friday, March 11, 2011, Time: 2:00 p.m.
Location: Fine Hall 801

Abstract:

In a periodic Lorentz gas a particle moves bouncing off a regular array of fixed convex obstacles (scatterers), like in a pinball machine. When the horizon is finite, one observes a classical diffusion law. When the obstacles are so large that the tunnels between them become narrow (of width $\epsilon \to 0$) then the diffusion matrix scales with $\epsilon$. In the limit, when $\epsilon=0$, the particle is trapped in a compact region with cusps in the boundary. In that case the system ceases to be uniformly hyperbolic and develops anomalies. Correlations decay slowly, as $1/n$, and the classical central limit theorem fails. Instead, a non-classical limit law holds, with a scaling factor of $\sqrt{n\log n}$ replacing the standard $\sqrt{n}$. However, for a special observables whose average values at the cusps vanish, the classical central limit law still holds.

Differential Geometry and Geometric Analysis Seminar

Topic:

CR moduli spaces on a contact 3-manifold

Presenter:

Jih-Hsin Cheng, Academia Sinica, Taiwan

Date: 

Friday, March 11, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

We study low-dimensional problems in topology and geometry via a study of contact and Cauchy-Riemann ($CR$) structures. In particular, we consider various $CR$ moduli spaces on a contact 3-manifold. A contact structure is called spherical if it admits a compatible spherical $CR$ structure. We will talk about spherical contact structures and our analytic tool, an evolution equation of $CR$ structures. We argue that solving such an equation for the standard contact 3-sphere is related to the Smale conjecture in 3-topology. Furthermore, we propose a contact analogue of Ray-Singer's analytic torsion. This ''contact torsion'' is expected to be able to distinguish among ''spherical space forms'' $\{\Gamma\backslash S^{3}\}$ as contact manifolds. Positivity of the $CR$ Paneitz operator becomes an important property in the study of recent years. We will investigate the relation between this property and the embeddability of $CR$ structures if we have enough time.

PACM Colloquium

Topic:

Brother, can you spare a compacton?

Presenter:

Philip Rosenau, Tel Aviv University

Date:

Monday, March 21, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Abstract:

Unlike certain personal or national tragedies which may extend indefinitely, patterns observed in nature are of finite extent. Yet, as a rule, the solitary patterns predicted by almost all existing mathematical models extend indefinitely with their tails being a by product of their analytical nature. Rather then viewing such tails as a manifestation of the inherent limitation of math to model physics in detail, we adopt the opposite view: the persistence of tails in a large variety of solitary patterns points to a missing mechanism capable to constrain the pattern. Clearly, to induce a compact pattern one has to escape the curse of analyticity. Differently stated, one has to supplement the existing models with a mechanism(s) which may beget a local singularity. When this is done the resulting local loss of solution's uniqueness enables to connect a smooth part of the solution with the trivial ground state and thus to form an entity with a compact support: the compacton. We shall describe a variety of singularity inducing mechanisms that beget compact solutions of dispersive or dissipative uni and multi-dimensional phenomena. Compactified variants of the K-dV, Klein-Gordon and Schroedinger equations will be surveyed. In Part two of the lecture we shall discuss the intriguing nature of these (weakly strong or strongly weak) solutions, the underlying singularities and their relation with a discrete antecedent where a sharp fronts are replaced with tails decaying at a doubly exponential rate.

Algebraic Topology Seminar **Please note special day and time**

Topic:

Massey Triple Products

Presenter:

Larry Taylor, IAS

Date: 

Tuesday, March 22, 2011, Time: 5:00 p.m., Location: Fine Hall 314

Abstract:

A technique will be discussed to control the indeterminacy in cohomology Massey triple products. A variety of non-vanishing and vanishing results for Massey triple products are proved using this technique. Here are three examples. • Many authors have noticed that non-trivial triple products in a submanifold produce non-trivial triple products in the blowup along the submanifold. • Given a map of closed, compact manifolds of the same dimension, f : M → N , then non- trivial triple products with field coefficients in N pull back to non-trivial triple products in M provided the degree of the map is non-zero in the field. • Given two classes x_1 and x_2 in an n-manifold, there is a dual pairing for triple products<x_1,?,x_2> between the image of this triple product in dimension r with the image in dimension n+|x_1|+|x_2|-1-r.

Ergodic Theory and Statistical Mechanics Seminar

Topic:

TBA

Presenter:

Corinna Ulcigrai, University of Bristol

Date: 

Thursday, March 24, 2011, Time: 2:00 p.m., Location: Fine Hall 801 (note change in room #)

Algebraic Topology Seminar

Topic:

TBA

Presenter:

Bill Browder, Princeton University

Date: 

Thursday, March 24, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Differential Geometry and Geometric Analysis Seminar

Topic:

Partial regularity of a minimizer of the relaxed energy for biharmonic maps

Presenter:

Min-Chun Hong, University of Queensland Brisbane

Date: 

Friday, March 25, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

In 1999, Chang, Wang and Yang established the fundamental result on the partial regularity stationary biharmonic maps into spheres. Since then, the study of biharmonic maps has attracted much attention. In this talk, we will discuss some new result on the relaxed energy for biharmonic maps from an $m$-dimensional domain into spheres for an integer $m\geq 5$. We prove that the minimizer of the relaxed energy of the Hessian energy is biharmonic and smooth outside a singular set $\Sigma$ of finite $(m-4)$-dimensional Hausdorff measure. Moreover, when $m=5$, we also show that the singular set $\Sigma$ is $1$-rectifiable.

Department Colloquium

Topic:

TBA

Presenter:

Yuri Tschinkel, NYU

Date: 

Wednesday, March 30, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Algebraic Topology Seminar

Topic:

An integral lift of the Gamma-genus

Presenter:

Jack Morava, Johns Hopkins University

Date: 

Thursday, March 31, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

The Hirzebruch genus of a complex-oriented manifold M associated (by Kontsevich) to Euler's Gamma-function has an analytic interpretation as the index of a family of deformations of a Dirac operator, parametrized by the homogeneous space Sp/U; in more homotopy-theoretic terms, it is the homomorphism

MU --> MU \smash_{MSp} KO

of ring spectra. It also has an interpretation as a kind of equivariant Euler characteristic of the free loopspace of M, suitably polarized. There are further intriguing connections with the theory of asymptotic expansions, involving the values of the zeta function at odd positive integers.

APRIL 2011

Differential Geometry and Geometric Analysis Seminar

Topic:

Geometrical variational problems in economics

Presenter:

Robert McCann, University of Toronto

Date: 

Friday, April 1, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Joint Analysis Seminar and PACM Colloquium

Topic:

TBA

Presenter:

Peter Jones, Yale University

Date:

Monday, April 4, 2011, Time: 4:00 p.m., Location: Fine Hall 214

PACM Colloquium - Distinguished Lecture Seminar **Please note special date**

Topic:

TBA

Presenter:

Ray Goldstein, Cambridge University

Date:

Wednesday, April 6, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Department Colloquium

Topic:

TBA

Presenter:

Thomas Haines, University of Maryland

Date: 

Wednesday, April 6, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Algebraic Topology Seminar

Topic:

Moment-angle complexes from simplicial posets

Presenter:

Taras Panov, Moscow State University

Date: 

Thursday, April 7, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Abstract:

The construction of moment-angle complexes may be extended from simplicial complexes to simplicial posets. As a result, a certain T^m-space Z_S is associated to an arbitrary simplicial poset S on m vertices. Face rings Z[S]$ of simplicial posets generalise those of simplicial complexes, but have much more complicated algebraic structure. These rings Z[S] may be studied by topological methods. The space Z_S has many important topological properties of the original moment-angle
complex Z_K associated to a simplicial complex K. In particular, the integral cohomology algebra of Z_S is isomorphic to the Tor-algebra of the face ring Z[S]. This leads directly to a generalisation of Hochster's theorem, expressing the algebraic Betti numbers of the ring Z[S] in terms of the homology of full subposets in S. Finally, the total amount of homology of Z_S may be estimated from below, which settles Halperin's toral rank conjecture for the moment-angle complexes Z_S.

Topology Seminar

Topic:

Geometric structures on moment-angle manifolds

Presenter:

Taras Panov, Moscow State University

Date: 

Thursday, April 7, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Abstract:

Moment-angle complexes are spaces acted on by a torus and parametrised by finite simplicial complexes. They are central objects in toric topology, and currently are gaining much interest in the homotopy theory. Due the their combinatorial origins, moment-angle complexes also find applications in combinatorial geometry and commutative algebra. Moment-angle complexes corresponding to simplicial subdivision of spheres are topological manifolds, and those corresponding to simplicial polytopes admit smooth realisations as intersection of real quadrics in C^m.

After an introductory part describing the general properties of moment-angle complexes we shall concentrate on the complex-analytic and Lagrangian aspects of the theory. We show that the moment-angle manifolds corresponding to complete simplicial fans admit nonKaehler complex-analytic structures. This generalises the known construction of complex-analytic structures on polytopal moment-angle manifolds, coming from identifying them as LVM-manifolds. We proceed by describing the Dolbeault cohomology and certain Hodge numbers of moment-angle manifolds by applying the Borel spectral sequence to holomorphic principal bundles over toric varieties.

A new wide family of minimal Lagrangian submanifolds N in C^m or CP^m can be constructed from intersections of real quadrics. These submanifolds have the following topological properties: every N embeds in the corresponding moment-angle manifold Z, and every N is the total space of two different fibrations, one over the torus T^{m-n} with fibre a real moment-angle manifold R, and another over a small cover with fibre a torus. These properties are used to produce new examples of Lagrangian submanifolds with quite complicated topology. Different parts of this talk are based on joint works with Victor Buchstaber, Andrei Mironov and Yuri Ustinovsky.

Differential Geometry and Geometric Analysis Seminar

Topic:

TBA

Presenter:

Dmitri Burago, Penn State

Date: 

Friday, April 8, 2011, Time: 3:00 p.m., Location: Fine Hall 314

PACM Colloquium

Topic:

From (basic) image denoising to surface evolution

Presenter:

Antonin Chambolle, CMAP -- Ecole Polytechnique

Date:

Monday, April 11, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Abstract:

It is relatively easy to make a connection between the implicit time-discrete approaches for the mean curvature flow and the "Rudin-Osher-Fatemi" total variation based approach for image denoising. This connection has interesting consequences, allowing to build explicit solutions for the flow of the total variation or study regularity issues, up to showing the existence of the crystalline curvature flow of convex sets or building up efficient algorithms. The talk will explain the relationship between all these problems. (Joint works with V. Caselles, M. Novaga, J. Darbon, T. Pock, D. Cremers)

Algebraic Geometry Seminar

Topic:

TBA

Presenter:

Mircea Mustaţă, U. of Michigan

Date:

Tuesday, April 12, 2011, Time: 4:30 p.m., Location: Fine Hall 322

Algebraic Topology Seminar **Please note special day and time**

Topic:

The Geometry of Music

Presenter:

Dmitri Tymoczko, Princeton University, Department of Music

Date: 

Tuesday, April 12, 2011, Time: 5:00 p.m., Location: Fine Hall 314

Abstract:

In my talk, I explain how to translate basic concepts of music theory into the language of contemporary topology and geometry. Musicians commonly abstract away from five kinds of musical information -- including the order, octave, and specific pitch level of groups of notes.  This process produces a family of quotient spaces or orbifolds: for example, two-note chords live on a Mobius strip, while three-note chord-types live on a cone.  These spaces provide a general geometrical framework for understanding and interpreting music.  Related constructions also appear naturally in other applied-math contexts, for instance in economics.

Department Colloquium

Topic:

TBA

Presenter:

Steve Zelditch, Northwestern University

Date: 

Wednesday, April 13, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Algebraic Topology Seminar

Topic:

On the rational homotopy type of Moment-angle complexes

Presenter:

Sam Gitler, IAS

Date: 

Thursday, April 14, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Differential Geometry and Geometric Analysis Seminar

Topic:

TBA

Presenter:

Richard Bamler, Princeton University

Date: 

Friday, April 15, 2011, Time: 3:00 p.m., Location: Fine Hall 314

PACM Colloquium

Topic:

TBA

Presenter:

Gregory Rempala, Medical College of Georgia

Date:

Monday, April 18, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Algebraic Geometry Seminar

Topic:

TBA

Presenter:

Charles Doran, U. Alberta

Date:

Tuesday, April 19, 2011, Time: 4:30 p.m., Location: Fine Hall 322

Department Colloquium

Topic:

TBA

Presenter:

Alexander Bufetov, Rice University

Date: 

Wednesday, April 20, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Ergodic Theory and Statistical Mechanics Seminar **please note change in room number**

Topic:

TBA

Presenter:

Alexander Bufetov, Rice University

Date: 

Thursday, April 21, 2011, Time: 2:00 p.m., Location: Fine Hall 801

Algebraic Topology Seminar

Topic:

Unstable operations in etale and motivic cohomology

Presenter:

Chuck Weibel, Rutgers University

Date: 

Thursday, April 21, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Princeton University and IAS Number Theory Seminar

Topic:

TBA

Presenter:

Henri Darmon, McGill University

Date: 

Thursday, April 21, 2011, Time: 4:30 p.m., Location: Fine Hall 214

PACM Colloquium

Topic:

TBA

Presenter:

Boaz Nadler, Weizmann Institute -- Israel

Date:

Monday, April 25, 2011, Time: 4:00 p.m., Location: Fine Hall 214

Algebraic Topology Seminar

Topic:

TBA

Presenter:

Victor Buchstaber, Steklov Mathematical Institute, Russian Academy of Sciences.

Date: 

Thursday, April 28, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Topology Seminar

Topic:

TBA

Presenter:

Peter Ozsvath, MIT

Date: 

Thursday, April 28, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Differential Geometry and Geometric Analysis Seminar

Topic:

TBA

Presenter:

Artem Pulemotov, Chicago

Date: 

Friday, April 29, 2011, Time: 3:00 p.m., Location: Fine Hall 314

MAY 2011

Department Colloquium

Topic:

TBA

Presenter:

Gautam Chinta, The City University of New York

Date: 

Wednesday, May 4, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Topology Seminar

Topic:

TBA

Presenter:

Liam Watson, UCLA

Date: 

Thursday, May 5, 2011, Time: 4:30 p.m., Location: Fine Hall 314

Differential Geometry and Geometric Analysis Seminar

Topic:

TBA

Presenter:

Yannick Slre, Universite de Aix-Marseille III

Date:

Friday, May 6, 2011, Time: 3:00 p.m., Location: Fine Hall 314

Department Colloquium

Topic:

TBA

Presenter:

Balazs Szegedy, University of Toronto

Date: 

Wednesday, May 11, 2011, Time: 4:30 p.m., Location: Fine Hall 314