| DIFFERENTIAL GEOMETRY SEMINAR: |
| LOK MING (RONALD) LUI (Harvard University): |
| Computational Differential Geometry and its application to Human Brain Mapping |
| on Tuesday, February 09, 2010, at 1:30 - 3:00 pm in Science Center, Room 507 |
| Abstract: In Human Brain Mapping, neuroscientists commonly aim to identify structural differences between healthy and unhealthy brains, in order to detect systematic patterns of alterations in brain diseases. Surface-based cortical analysis is an important strategy and has found useful applications in disease analysis. The main obstacle is that the human brain cortical surface is a very complicated manifold with difficult geometry. In this talk, I will describe how conformal and quasiconformal geometry can be used to analyze brain structures accurately and systematically. I will firstly describe how conformal and quasiconformal maps can be computed. These maps give the best global parameterizations of cortical surfaces which align landmarks and ca n be used for various applications such as surface registration, feature detection, computation on surfaces, etc. Secondly, different surfaces with landmarks correspondence have different conformal structures. This gives a signature for different brain surfaces for shape analysis. In the second part of my talk, I will describe how conformal structure of the brain surface can be used for shape analysis. Specifically, I will describe how different conformal modules can be computed and used for abnormality detection in brain surfaces. This seminar is organized by Professor Shing-Tung Yau. |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY: |
| DENNIS GAITSGORY (Harvard University): |
| Overview and recap of Dustin's talk on quantization |
| on Tuesday, February 09, 2010, at 5:30 - 8:00 pm in Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: |
| MANISH PATNAIK (Harvard University): |
| Geometry of arithmetic quotients of loop groups |
| on Tuesday, February 09, 2010, at 3 pm in Science Center, Room 507 |
| The moduli of G-bundles on a curve over a field of finite characteristic admits a description in terms of an arithmetic quotient of the adelic points of the group G. Replacing G by its loop group and considering an analogous arithmetic quotient, we will explain how the resulting set parametrizes G-bundles on certain algebraic surfaces together with information about the second Chern class of such bundles. The main ingredient will be an adelic Riemann-Roch type formula relating the central extension of loop groups and the K-theoretic second Chern class. We will also try to explain the connection with Eisenstein series on loop groups. This is joint work with Howard Garland. |
| NUMBER THEORY SEMINAR: |
| ZHIWEI YUN (): |
| From automorphic forms to Klooserman sheaves |
| on Wednesday, February 10, 2010, at 3 - 4 pm in Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS: |
| HOI H. NGUYEN (Rutgers University): |
| On the inverse Littlewood-Offord problem |
| on Thursday, February 11, 2010, at 3:10 pm in Science Center, Room 232 |
| GAUGE THEORY AND TOPOLOGY: |
| ALEX SUBOTIC (Harvard University): |
| A monoidal structure for Fukaya categories |
| on Friday, February 12, 2010, at 3:30 - 4:30 pm in Science Center, Room 507 |
| DIFFERENTIAL GEOMETRY SEMINAR: |
| MBOYO ESOLE (Harvard University): |
| F-theory and new types of singular fibers for elliptic fibrations |
| on Tuesday, February 16, 2010, at 1:30 - 3:00 pm in MIT (2-190) |
| Abstract: F-theory was invented by Vafa to describe the strong coupling limit of type IIB string theory. Mathematically, it is an elegant physical formulation of the geometric structure of elliptic fibrations. Singular fibers play an essential role in F-theory. Singular fibers of an elliptic surface have been classified by Kodaira and Neron. This classification have been generalized to elliptically threefolds by Miranda and more recently to elliptic n-fold by Szydlo. Miranda and Szydlo classifications rely on conditions of normal crossing and require a well defined j-invariant all over the base of the elliptic fibration. However, for physically interested cases, one has to go above these conditions. This transgression opens the door to new types of fibers. F-theory provides a setting to discuss these new singular fibers. I will present the derivation of some of these new types of singular fibers not present in previous classifications. They have an interesting link with generalization of Neron models to base with non-perfect residue field and characteristic different from zero. The new fibers often also have a simple description in terms of folding of extended Dynkin diagram by certain automorphisms. As a reward, I will present a systematic resolution of the singular Weierstrass model describing the SU(5) Grand Unified Theory. Differential Geometry Seminars are organized by Professor Shing-Tung Yau. |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY: |
| RYAN REICH (Harvard University): |
| Affine Grassmannian-I: factorization, convolution and fusion |
| on Tuesday, February 16, 2010, at 5:30 - 8:00 pm in Science Center, Room 507 |
| NUMBER THEORY SEMINAR: |
| MARK REEDER (): |
| Supercuspidal representations and invariant theory |
| on Wednesday, February 17, 2010, at 3 - 4 pm in Science Center, Room 507 |
| RANDOM MATRIX AND PROBABILITY SEMINARS: |
| C. BORGS (Microsoft ): |
| Polya Urns and Convergence of Preferential Attachment Graphs |
| on Thursday, February 18, 2010, at 3:10 pm in Science Center, Room 232 |
| Abstract: After discussing general notions of graph sequences, including the Benjamini-Schramm limit of a sequence of graphs, I introduce a new representation for preferential attachments graphs related to an old concept from probability, the notion of Polya urns. Using this new representation, we then construct the Benjamini-Schramm limit of a sequence of preferential attachment graphs. The work presented in this talk is joint work with N. Berger, J.T. Chayes and A. Saberi. |
| JOINT BRANDEIS-HARVARD-MIT NORTHEASTERN MATHEMATICS COLLOQUIUM: |
| ZHOUPING XIN (The Chinese University of Hong Kong): |
| Mixed Type Equations and Compressible Transonic Flows |
| on Thursday, February 18, 2010, at 4:30 pm in Science Center, Hall D |
| Abstract: The mathematical theory of systems of multi-dimensional huperbolic conservations remains a great challenge to the field of nonlinear partial differential equations. Some of the main difficulties in dealing with such a system are the system is mixed type and may change types so that the classical approaches fail to yield the global well-posedness theory. This is so even for the important compressible Euler systems in gas dynamics. In this talk, I will illustrate these by the example of the transonic steady compressible flows in multi-dimensional ducts with variable sections. In particular, I will discuss some recent progress on the transonic shock problem in a class de Laval nozzles due to Courant-Friedrichs and existence of smooth subsonic-sonic and transonic flows in such nozzles. |
| GAUGE THEORY AND TOPOLOGY: |
| ZHONGTAO WU (Princeton): |
| Cosmetic Surgery Conjecture for S^3 |
| on Friday, February 19, 2010, at 3:30 - 4:30 pm in Science Center, Room 507 |
| BASIC NOTIONS SEMINAR: |
| ANTTI KNOWLES (Harvard University): |
| TBA |
| on Monday, February 22, 2010, at 3 pm in Science Center, Room 507 |
| Basic Notions Seminars are organized by Professor Shing-Tung Yau. |
| HARVARD/MIT GRADUATE STUDENT SEMINAR IN GEOMETRIC REPRESENTATION THEORY: |
| RYAN REICH (Harvard University): |
| Affine Grassmannian-II: geometric Satake equivalence |
| on Tuesday, February 23, 2010, at 5:30 - 8:00 pm in Science Center, Room 507 |
| HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: |
| CURT MCMULLEN (Harvard University): |
| K3 surfaces , entropy and glue |
| on Tuesday, February 23, 2010, at 3 pm in Science Center, Room 507 |
| NUMBER THEORY SEMINAR: |
| MATT BAKER (Georgia Institute of Technology): |
| Complex dynamics and adelic potential theory |
| on Wednesday, February 24, 2010, at 3 - 4 pm in Science Center, Room 507 |
| Abstract: Using tools from number theory and complex analysis, Laura DeMarco and I have recently proved the following theorem: for any fixed complex numbers a and b, and any integer d at least 2, the set of complex numbers c for which both a and b are preperiodic for z^d+c is infinite if and only if a^d=b^d. This provides an affirmative answer to a question of Zannier. The main arithmetic ingredient in the proof is an adelic equidisrtibution theorem for preperiodic points over number fields and function fields, with non-archimedean Berkovich spaces playing an essential role. |
| NUMBER THEORY SEMINAR: |
| BENOIT STROH (): |
| Compactification of Siegel varieties at some places of bad reduction |
| on Wednesday, March 03, 2010, at 3 - 4 pm in Science Center, Room 507 |
| NUMBER THEORY SEMINAR: |
| A. GONCHAROV (Brown University): |
| Hodge correlators and Rankin-Selberg integrals |
| on Wednesday, March 10, 2010, at 3 - 4 pm in Science Center, Room 507 |
| NUMBER THEORY SEMINAR: |
| ROBERT POLLACK (BU): |
| Fitting ideals of Selmer groups of modular forms |
| on Wednesday, March 31, 2010, at 3 - 4 pm in Science Center, Room 507 |
| NUMBER THEORY SEMINAR: |
| BJORN POONEN (): |
| Neron-Severi groups under specialization |
| on Wednesday, April 14, 2010, at 3 - 4 pm in Science Center, Room 507 |
| This is a joint work with Davesh Maulik and Claire Voisin |
| NUMBER THEORY SEMINAR: |
| PHAM TIEP (Arizona State University): |
| Representations of finite simple groups and applications |
| on Wednesday, April 28, 2010, at 3 - 4 pm in Science Center, Room 507 |
| Abstract: In the first part of the talk we will survey recent results on representations of finite (quasi) simple groups. In the second part we will describe some applications of these results in group theory and algebraic geometry. In particular, we will discuss recent proofs by the speaker and his collaborators of some conjectures of Katz, Kollar, Larsen, and Ore. |
| NUMBER THEORY SEMINAR: |
| PASCAL BOYER (): |
| TBA |
| on Wednesday, May 05, 2010, at 3 - 4 pm in Science Center, Room 507 |