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MARCH 2011 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Ergodic properties of infinite extensions of area-preserving flows |
Presenter: |
Corinna Ulcigrai, University of Bristol |
Date: |
Thursday, March 24, 2011, Time: 2:00 p.m., Location: Fine Hall 801 |
Abstract: |
We consider infinite volume preserving flows that are obtained as extensions of flows on surfaces. Consider a smooth area-preserving flow on a surface S given by a vector field X and consider a real valued function f on X. The (skew-product) extension of the flow on S given by f is the flow on S x R given by the solutions to the differential equations dx/dt=X, dy/dt=f, where (x,y) are coordinates on S x R and R is the real line. While the ergodic properties of surface flows that preserve a smooth area form are now well understood (as we will summarize), very little is known for these infinite measure preserving extensions, which were previously studied only when S is a torus. We prove ergodicity of the infinite extension when the surface flow is of periodic type and f belong to a suitable subspace of smooth functions. In the proof we develop renormalization techniques for cocycles with logarithmic singularities over interval exchange transformations. This is joint work with K. Fraczek. |
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Algebraic Topology Seminar |
Topic: |
Equivariant cohomology and orbit structure |
Presenter: |
Matthias Franz, University of Western Ontario |
Date: |
Thursday, March 24, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
Abstract: |
Let T be a torus, and let X be a T-space. In this talk I will relate algebraic properties of the equivariant (co)homology of X to the structure of the T-orbits in X. This generalizes a result of Atiyah and Bredon. As applications, I will characterize those compact T-manifolds which admit a Chang-Skjelbred (or GKM) description of their equivariant cohomology, and also those for which the equivariant Poincaré pairing is perfect. This is joint work with Chris Allday and Volker Puppe. |
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Joint IAS and Princeton University Number Theory Seminar **please note different location** |
Topic: |
Random maximal isotropic subspaces and Selmer groups |
Presenter: |
Bjorn Poonen, MIT |
Date: |
Thursday, March 24, 2011, Time: 4:30 p.m., Location: IAS - Room S101 |
Abstract: |
We show that the p-Selmer group of an elliptic curve is naturally the intersection of two maximal isotropic subspaces in an infinite-dimensional locally compact quadratic space over F_p. By modeling this intersection as the intersection of a random maximal isotropic subspace with a fixed compact open maximal isotropic subspace, we can explain the known phenomena regarding distribution of Selmer ranks, such as the theorems of Heath-Brown, Swinnerton-Dyer, and Kane for 2-Selmer groups in certain families of quadratic twists, and the average size of 2- and 3-Selmer groups as computed by Bhargava and Shankar. The random model is consistent with Delaunay's heuristics for Sha[p], and predicts that the average rank of elliptic curves is at most 1/2. This is joint work with Eric Rains. |
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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. |
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Department Colloquium |
Topic: |
Rational points on algebraic varieties |
Presenter: |
Yuri Tschinkel, NYU |
Date: |
Wednesday, March 30, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
I will discuss several geometric techniques and constructions that emerged in the study of rational points on higher-dimensional algebraic varieties over global fields |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
Bifurcations of solutions of the 2-dimensional Navier-Stokes system |
Presenter: |
Dong Li, University of Iowa |
Date: |
Thursday, March 31, 2011, Time: 2:00 p.m., Location: Fine Hall 801 |
Abstract: |
I will explain recent joint work with Sinai on the bifurcations of solutions to the 2-dimensional Navier-Stokes system |
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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. |
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Topology Seminar |
Topic: |
Pseudo-Anosov maps with small dilatation |
Presenter: |
Joan Birman, Columbia University |
Date: |
Thursday, March 31, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
Fix an orientable surface $S$. It is known that the set of dilatations of all pseudo-Anosov maps acting on $S$ is a family of real numbers that is bounded below by 1, and has a minimum value $\lambda_{min,S}>1$ which is realized geometrically. We will discuss recent work on the problem of determining $\lambda_{min,S}$ and show how a little-known theorem, the `Coefficient Theorem for Digraphs',can be used to gain insight into this set. The study of small dilatation pA maps appears to be related to the study of small volume fibered hyperbolic 3-manifolds, and an example from 3-manifolds has played a role in understanding the dilatation problem. |
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APRIL 2011 |
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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 |
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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 |
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Algebraic Topology Seminar **please note special day and time** |
Topic: |
Compact aspherical manifolds whose fundamental groups have center |
Presenter: |
Sylvain Cappell, NYU |
Date: |
Tuesday, April 5, 2011, Time: 5:00 p.m., Location: Fine Hall 314 |
Abstract: |
Classical work of Borel had shown that an action of the circle on a manifold with contractible universal cover yields non-trivial center in the manifold's fundamental group. In the early 70's, Conner and Raymond made further deep investigations which led them to conjecture a converse to Borel's result. We construct counter-examples to this conjecture, i.e., we exhibit aspherical manifolds (in all dimensions greater than or equal to 6) which have non-trivial center in their fundamental groups but no circle actions (and hence no compact Lie group actions). The constructions involve synthesizing rather disparate methods of geometric topology, geometric group theory and hyperbolic geometry. (This is joint work with Shmuel Weinberger and Min Yan.) |
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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 |
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Department Colloquium |
Topic: |
Endoscopic transfer of the Bernstein center |
Presenter: |
Thomas Haines, University of Maryland |
Date: |
Wednesday, April 6, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
The Langlands-Shelstad theory of endoscopy plays a central role in the study of Shimura varieties and the Arthur-Selberg trace formula. The fundamental lemma and a deep consequence, endoscopic transfer, have now been established in works of Ngo, Waldspurger, and Hales. Both of these statements are identities involving orbital integrals of a function $f$ on a $p$-adic group $G$ and those of certain "transfer" functions $f^H$ on related groups $H$, called endoscopic. This talk will give background on the fundamental lemma, some of its variants, and the roles they played. Then I will describe a conjectural construction of a large class of matching functions in the Bernstein centers of $G$ and $H$. This conjecture has been verified in some encouraging cases. The functions being transferred arise in connection with Shimura varieties with bad reduction, and some applications to that subject will also be briefly discussed. |
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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 |
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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. |
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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 |
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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). |
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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 |
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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. |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Steve Zelditch, Northwestern University |
Date: |
Wednesday, April 13, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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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 |
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Topology Seminar |
Topic: |
The Rank versus Genus Conjecture |
Presenter: |
Tao Li, Boston College |
Date: |
Thursday, April 14, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
Abstract: |
We construct a counterexample to the Rank versus Genus Conjecture (also known as the Rank Conjecture), i.e., a closed orientable hyperbolic 3-manifold with rank of its fundamental group smaller than its Heegaard genus. |
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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 |
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PACM Colloquium |
Topic: |
Likelihood and algebraic maps for stochastic biochemical network models |
Presenter: |
Gregory Rempala, Medical College of Georgia |
Date: |
Monday, April 18, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
With the development of new sequencing technologies of modern molecular biology, it is increasingly common to collect time-series data on the abundance of molecular species encoded within the genomes. This presentation shall illustrate how such data may be used to infer the parameters as well as the structure of the biochemical network under mass-action kinetics. Given certain constraints on the geometry of the stoichiometric space, we use algebraic methods as an alternative to conventional hierarchical graphical models, to carry out network structure inference by identifying reaction rate constants which are significantly different from zero. |
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Algebraic Geometry Seminar |
Topic: |
TBA |
Presenter: |
Charles Doran, University of Alberta |
Date: |
Tuesday, April 19, 2011, Time: 4:30 p.m., Location: Fine Hall 322 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Alexander Bufetov, Rice University |
Date: |
Wednesday, April 20, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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Ergodic Theory and Statistical Mechanics Seminar |
Topic: |
TBA |
Presenter: |
Alexander Bufetov, Rice University |
Date: |
Thursday, April 21, 2011, Time: 2:00 p.m., Location: Fine Hall 801 |
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Discrete Mathematics Seminar |
Topic: |
TBA |
Presenter: |
Paul Wollan, Sapienza University of Rome and Georgia Tech |
Date: |
Thursday, April 21, 2011, Time: 2:15 p.m., Location: Fine Hall 224 |
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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 |
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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 |
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PACM Colloquium |
Topic: |
Learning from Labeled and Unlabeled Data: Global vs. Multiple Approaches |
Presenter: |
Boaz Nadler, Weizmann Institute - Israel |
Date: |
Monday, April 25, 2011, Time: 4:00 p.m., Location: Fine Hall 214 |
Abstract: |
In recent years there is increasing interest in learning from both labeled and unlabeled data (a.k.a. semi-supervised learning, or SSL). The key assumption in SSL, under which an abundance of unlabeled data may help, is that there is some relation between the unknown response function to be learned and the marginal density of the predictor variables. In the first part of this talk I'll present a statistical analysis of two popular graph based SSL algorithms: Laplacian regularization method and Laplacian eigenmaps. In the second part I'll present a novel multiscale approach for SSL as well as supporting theory. Some intimate connections to harmonic analysis on abstract data sets will be discussed. Joint work with Nati Srebro (TTI), Xueyuan Zhou (Chicago), Matan Gavish (WIS/Stanford) and Ronald Coifman (Yale). |
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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 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Peter Ozsvath, MIT |
Date: |
Thursday, April 28, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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Differential Geometry and Geometric Analysis Seminar |
Topic: |
TBA |
Presenter: |
Artem Pulemotov, University of Chicago |
Date: |
Friday, April 29, 2011, Time: 3:00 p.m., Location: Fine Hall 314 |
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MAY 2011 |
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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 |
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Topology Seminar |
Topic: |
TBA |
Presenter: |
Liam Watson, UCLA |
Date: |
Thursday, May 5, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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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 |
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Department Colloquium |
Topic: |
TBA |
Presenter: |
Balazs Szegedy, University of Toronto |
Date: |
Wednesday, May 11, 2011, Time: 4:30 p.m., Location: Fine Hall 314 |
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