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Since fall 2005, "Basic Notions Seminars" are also called "Faculty
Colloquia". In these events, faculty members and sometimes guests of the department
give general talks on areas of research that interest them. These
talks are aimed at beginning graduate students, but everyone is welcome.
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Spring 2015
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Apr 20, 2015 | 3 PM | SC 507 | Dennis Gaitsgory | Langlands correspondence via shtukas, after V.Drinfeld, L.Lafforgue and V. Lafforgue |  |
Mon,Apr 06, 2015 | 3 PM | SC 507 | Shing-Tung Yau | Period integrals of algebraic manifolds and their differential equations (joint work with Bong Lian and An Huang) |
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Mon,Mar 23, 2015 | 3 PM | SC 507 | Brian Conrad | The arithmetic Lefschetz Principle |  |
Mon,Mar 09, 2015 | 3 PM | SC 507 | Jacob Lurie | Representation theory between characteristic Zero and Characteristic p |
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Mon,Mar 02, 2015 | 3 PM | SC 507 | Michael Rapoport | On accessible p-adic period domains |  |
Mon,Feb 23, 2015 | 3 PM | SC 507 | Daniel Cristofaro-Gardiner | Length and volume on contact three-manifolds |
Fall 2014
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Sep 22, 2014 | 3 PM | SC 507 | Benedict Gross | Singular moduli |  |
Mon,Oct 06, 2014 | 3 PM | SC 507 | Laure Saint-Raymond | The role of boundary layers in the global ocean circulation |
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Mon,Oct 20, 2014 | 3 PM | SC 507 | Hector Pasten | Uniform Diophantine undecidability |  |
Mon,Nov 03, 2014 | 3 PM | SC 507 | Joe Harris | Plane Curves |
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Mon,Nov 17, 2014 | 3 PM | SC 507 | Wilfried Schmid | A new look at mixed Hodge modules |
Spring 2014
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Apr 21, 2014 | 3 PM | SC 507 | Yum-Tong Siu | Methods of deltabar estimates in complex and algebraic geometry |  |
Mon,Apr 14, 2014 | 3 PM | SC 507 | Aaron Pixton | The cohomology of the moduli space of curves |
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Mon,Mar 31, 2014 | 3 PM | SC 507 | Joe Harris | Uniformity of rational points and the Lang conjecture |  |
Mon,Mar 10, 2014 | 3 PM | SC 507 | Yaiza Canzani | Local geometry of the nodal sets of Laplace eigenfunctions |
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Mon,Mar 03, 2014 | 3 PM | SC 507 | Hugh Woodin | The Continuum Hypothesis and the conception of mathematical infinity |  |
Mon,Feb 24, 2014 | 3 PM | SC 507 | Andrew Cotton-Clay | Weinstein Manifolds |
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Mon,Feb 10, 2014 | 3 PM | SC 507 | Dennis Gaitsgory | Drinfeld's shtukas and related ideas |
Fall 2013
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Dec 09, 2013 | 3 PM | SC 507 | Benedict Gross | On the arithmetic of hyperelliptic curves |  |
Mon,Nov 2013 | 3 PM | SC 507 | Arul Shankar | Counting Binary cubic forms using geometry-of-numbers techniques |
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Mon,Nov 18, 2013 | 3 PM | SC 507 | Shing-Tung Yau | 150 Years of Mathematics at Harvard |  |
Mon,Nov 04, 2013 | 3 PM | SC 507 | Curt McMullen | Complex hyperbolic geometry of moduli spaces |
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Mon,Oct 21, 2013 | 3 PM | SC 507 | Hiro Tanaka | Factorization homology and link invariantses | |
Mon,Sep 30, 2013 | 3 PM | SC 507 | Jacob Lurie | Artin Reciprocity via Algebraic K-Theory |
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Mon,Sep 23, 2013 | 3 PM | SC 507 | Joe Harris | How flexible are curves in projective space? |  |
Mon,Sep 16, 2013 | 3 PM | SC 507 | Alex Kontorovich | Level of distribution |
Spring 2013
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Mar 25, 2013 | 3 PM | SC 507 | Mark Kisin | The Grothendieck p-curvature conjecture | |
Mon,Mar 04, 2013 | 3 PM | SC 507 | Dennis Gaitsgory | Induction of representations and weird Frobenius reciprocity |
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Mon,Feb 25, 2013 | 3 PM | SC 507 | Igor Rodnianski | Nonlinear scattering for black holes |  |
Mon,Feb 11, 2013 | 3 PM | SC 507 | Mboyo Esole | The Geometry of Elliptic Fibrations, a String Theory Perspective |
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Mon,Mar 04, 2013 | 3 PM | SC 507 | Dan Stroock (MIT) | Randomness and Regularity |  |
Mon,Apr 15, 2013 | 3 PM | SC 507 | Albrecht Klemm (University of Bonn) | The refined BPS index from stable pair invariants |
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Mon,Apr 22, 2013 | 3 PM | SC 507 | Richard Melrose (MIT) | Fusion, Loop-Spin and String structures |
Fall 2012
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Nov 26, 2012 | 3 PM | SC 507 | Sukhada Fadnavis | A Generalization of the Birthday Problem |  |
Mon,Nov 19, 2012 | 3 PM | SC 507 | Emily Riehl | Weighted limits and colimits |
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Mon,Oct 29, 2012 | 3 PM | SC 507 | Fan Chung Graham | Can you hear the shape of a network? |  |
Mon,Oct 22, 2012 | 3 PM | SC 507 | Shlomo Sternberg | Recent Incarnations of the Cartan Three form |
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Mon,Sep 24, 2012 | 3 PM | SC 507 | Siu-Cheong Lau | Mirror symmetry and Fourier transform | |
Mon,Sep 17, 2012 | 3 PM | SC 507 | Sing-Tung Yau | Geometry of singular Einstein space |
Spring 2012
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Feb 6, 2012 | 3 PM | SC 507 | HT Yau | Random Matrix, Beta ensembles, and Dyson Brownian Motion | |
Mon,Feb 13, 2012 | 3 PM | SC 507 | Benedict Gross | Discriminants and root discriminants |
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Mon,Feb 27, 2012 | 3 PM | SC 507 | Barry Mazur | Statistics of arithmetic of elliptic curves | |
Mon,Mar 05, 2012 | 3 PM | SC 507 | Wilfried Schmid | Mixed Hodge modules |
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Mon,Mar 19, 2012 | 3 PM | SC 507 | Viabhav Gadre | Word and relative metrics along random geodesics |  |
Mon,Mar 26, 2012 | 3 PM | SC 507 | Sophie Morel | Langlands Functoriality |
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Mon,Apr 02, 2012 | 3 PM | SC 507 | Keerthi Madapusi Pera | p-adic uniformization and Hodge cycles on abelian varieties | |
Mon,Apr 09, 2012 | 3 PM | SC 507 | Yum-Tong-Siu | Multiplier Ideal Scheaves |
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Mon,Apr 16, 2012 | 3 PM | SC 507 | Alex Bloemendal | Continuum limits of random matrices at the spectral edge |  |
Mon,Apr 23, 2012 | 3 PM | SC 507 | Paul Bourgade | The circular law |
Fall 2011
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Nov 28, 2011 | 3 PM | SC 507 | David Kazhdan | Quivers and quantum groups | |
Mon,Nov 21, 2011 | 3 PM | SC 507 | Mark Kisin | "The Tate conjecture" |
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Mon,Nov 14, 2011 | 3 PM | SC 507 | Nir Avni | "Invariant Random Subgroups" |  |
Mon,Nov 7, 2011 | 3 PM | SC 507 | Cliff Taubes | "Differential equations, compactness and topology" |
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Mon,Oct 31, 2011 | 3 PM | SC 507 | Jacob Lurie | "Dijkgraaf-Witten models and vanishing theorems for higher Tate cohomology" |  |
Mon,Oct 24, 2011 | 3 PM | SC 507 | Peter Kronheimer | A recent history of the 4-dimensional Poincare conjecture |
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Mon,Oct 17, 2011 | 3 PM | SC 507 | Gerald Sacks | Models of set theory via measure theory |  |
Mon,Oct 3, 2011 | 3 PM | SC 507 | Jean-Pierre Serre | Integration and Equidistribution |
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Mon,Sep 26, 2011 | 3 PM | SC 507 | Noam Elkies | Covers of the Riemann sphere branched at few points | |
Mon,Sep 12, 2011 | 3 PM | SC 507 | Joe Harris | Brill-Noether Theory |
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Mon,Sep 19, 2011 | 3 PM | SC 507 | Dennis Gaitsgory | Contractibility of the space of rational maps |
Spring 2011
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Jan 31, 2011 | 3 PM | SC 507 | Lars Anderson | The black hole stability problem |  |
Mon,Feb 7, 2011 | 3 PM | SC 507 | Chen-Yu Chi | Singularities of hypersurfaces and the image of pluricanonical maps -- a metrical approach |
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Mon,Feb 14, 2011 | 3 PM | SC 507 | Gabor Lippner | Eigenvalue multiplicity and the genus of graphs |  |
Mon,Feb 28, 2011 | 3 PM | SC 507 | Rachel Epstein | The structure of the computably enumerable sets |
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Mon,Mar 21, 2011 | 3 PM | SC 507 | Laszlo Erdos | Large atoms and molecules in a self-generated magnetic field | |
Mon,Mar 28, 2011 | 3 PM | SC 507 | Jacob Lurie | Tamagawa numbers via nonabelian Poincare duality |
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Mon,Apr 4, 2011 | 3 PM | SC 507 | Li-Sheng Tseng | Similarities between complex and symplectic analysis |  |
Mon,Apr 11, 2011 | 3 PM | SC 507 | Joe Rabinoff | Implicitization via harmonic analysis on graphs, non-Archimedean analytic curves, and tropicalization |
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Mon,Apr 18, 2011 | 3 PM | SC 507 | Miranda Cheng | The sporadic group M24 and (Mock) Automorphic forms |
Fall 2010
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Sep 13, 2010 | 3 PM | SC 507 | Faculty | Basic Notions Job Search Seminar | |
Mon,Sep 20, 2010 | 3 PM | SC 507 | Curt McMullen | The Evolution of Geometric Structures on 3-Manifolds |
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Mon,Sep 27, 2010 | 3 PM | SC 507 | Joe Harris | Galois Groups in Geometry |  |
Mon,Oct 4, 2010 | 3 PM | SC 507 | Michael Rapoport | Period domains over finite and p-adic fields |
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Mon,Oct 18, 2010 | 3 PM | SC 507 | Benedict Gross | Automorphisms of root lattices | |
Mon,Oct 25, 2010 | 3 PM | SC 507 | Peter Kronheimer | Knots, links and Khovanov homology |
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Mon,Nov 1, 2010 | 3 PM | SC 507 | Paul Bourgade | Extreme spacings in random spectra |  |
Mon,Nov 8, 2010 | 3 PM | SC 507 | Helene Esnault, Universität Duisberg-Essen | Rational points and motivic integration |
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Mon,Nov 15, 2010 | 3 PM | SC 507 | Vaibhav Gadre | Length spectra for pseudo-Anosov maps: bounds for low dilatation examples | |
Mon,Nov 29, 2010 | 3 PM | SC 507 | Horng-Tzer Yau | Random matrices: a review of its history and the conjectures by Wigner and Dyson |
Spring 2010
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Feb 1, 2010 | 3 PM | SC 507 | Barry Mazur | Hilbert's 10th Problem and Elliptic Curves |  |
Mon,Feb 8, 2010 | 3 PM | SC 507 | Thomas Spencer (Princeton) | Random band matrices, statistical mechanics and hyperbolic symmetry |
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Mon,Feb 22, 2010 | 3 PM | SC 507 | Antti Knowles | Controlling quantum fluctuations in the mean-field limit |  |
Mon,Mar 1, 2010 | 3 PM | SC 507 | Yakov Sinai (Princeton) | Smoothness of solutions of the Navier-Stokes System inside the square |
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Mon,Mar 8, 2010 | 3 PM | SC 507 | Xinyi Yuan | Preperiodic points and p-adic Calabi theorem |  |
Mon,Mar 22, 2010 | 3 PM | SC 507 | Xinwen Zhu | Integral homology of loop groups via Langlands dual groups |
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Mon,Mar 29, 2010 | 3 PM | SC 507 | Arthur Ogus | Logarithmic Geometry |  |
Mon,Apr 5, 2010 | 3 PM | SC 507 | Wei Zhang | Absolutely Hodge Cycle |
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Mon,Apr 12, 2010 | 3 PM | SC 507 | Sarah Koch | Thurston's topological characterization of rational functions |  |
Mon,Apr 19, 2010 | 3 PM | SC 507 | Kristen Wickelgren | Grothendieck's Anabelian Conjectures |
Fall 2009
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Sep 14, 2009 | 3 PM | SC 507 | Faculty | Basic Notions Job Search Seminar | |
Mon,Sep 21, 2009 | 3 PM | SC 507 | Benedict Gross | Self-dual and conjugate-dual Galois representations |
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Mon,Sep 28, 2009 | 3 PM | SC 507 | Jacob Lurie | Categorification of the Fourier Transform | |
Mon,Nov 2, 2009 | 3 PM | SC 507 | Hao Xu | Intersection theory on moduli spaces of curves |
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Mon,Oct 19, 2009 | 3 PM | SC 507 | Cedric Villani | Landau damping | |
Mon,Oct 26, 2009 | 3 PM | SC 507 | HT Yau | Eigenvalue distributions of random matrices, a dynamical approach |
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Mon,Nov 9, 2009 | 3 PM | SC 507 | Wilfried Schmid | Hodge theory and unitary representations of reductive Lie groups | |
Mon,Nov 16, 2009 | 3 PM | SC 507 | Joseph Rabinoff | Beyond Newton polygons: locating the zeros of polynomials over a non-Archimedean field |
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Mon,Nov 23, 2009 | 3 PM | SC 507 | Dennis Gaitsgory | Quantum Langlands |  |
Mon,Nov 30, 2009 | 3 PM | SC 507 | Clark Barwick | Descent Problems for K-Theory |
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Mon,Dec 7, 2009 | 3 PM | SC 507 | Andrew Cotton-Clay | Symplectic field theory, tightness, and dynamics of vector fields | |
Mon,Feb 1, 2010 | 3 PM | SC 507 | Barry Mazur | Hilbert's 10th Problem and Elliptic Curves |
Spring 2009
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Feb 2, 2009 | 3 PM | SC 507 | Gerald Sacks | Infinitely Long Formulas: A Short Introduction |  |
Mon,Feb 9, 2009 | 3 PM | SC 507 | Thomas Lam | The Edrei-Thoma Theorem |
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Mon,Feb 23, 2009 | 3 PM | SC 507 | Martin Nowak and Corina Tarnita | Evolutionary Dynamics on Sets | |
Mon,Mar 2, 2009 | 3 PM | SC 507 | Noam Elkies | How to Solve Diophantine Equations |
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Mon,Mar 9, 2009 | 3 PM | SC 507 | Benedict Gross | Connections on Complex Algebraic Curves |  |
Mon,Mar 16, 2009 | 3 PM | SC 507 | John Duncan | Poincare Series |
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Mon,Mar 30, 2009 | 3 PM | SC 507 | Daniela Damjanovic | Perturbations of some higher rank unipotent actions | |
Mon,Apr 6, 2009 | 3 PM | SC 507 | Li-Sheng Tseng | Non-Kahler Geometry |
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Mon,Apr 13, 2009 | 3 PM | SC 507 | Lydia Bieri | Geometric Analysis and General Relativity |  |
Mon,Apr 20, 2009 | 3 PM | SC 507 | Jun Yin | Mathematical problems in quantum many-body physics |
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Mon,Apr 27, 2009 | 3 PM | SC 507 | Alice Guionnet | Random matrices, free probability and enumerations of maps |  |
Mon,May 11, 2009 | 3 PM | SC 507 | Michael Hopkins | The Kervaire invariant problem |
Fall 2008
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Sep 29, 2008 | 3 PM | SC 507 | Dennis Gaitsgory | Geometric representation theory | |
Mon,Oct 06, 2008 | 3 PM | SC 507 | Cliff Taubes | Inexpensive quantum field theories |
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Mon,Oct 20, 2008 | 3 PM | SC 507 | Nir Avni | Motivic Integration | |
Mon,Oct 27, 2008 | 3 PM | SC 507 | Joe Harris | The interpolation problem |
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Mon,Nov 3, 2008 | 3 PM | SC 507 | Peter Kronheimer | Using instantons to see the Thurston norm | |
Mon,Nov 10, 2008 | 3 PM | SC 507 | Clark Barwick | Schematic Homotopy Types |
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Mon,Nov 17, 2008 | 3 PM | SC 507 | Lauren Williams | What does the non-negative part of a flag variety look like? | |
Mon,Dec 8, 2008 | 3 PM | SC 507 | Shing-Tung Yau | Conserved quantities in classical general relativity |
Spring 2008
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Apr 14, 2008 | 3 PM | SC 507 | Cumrun Vafa | Topological Strings |  |
Mon,Apr 7, 2008 | 3 PM | SC 507 | Alberto de Sole | Hamiltonian equation, their integrals of motion and related algebraic structure. |
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Mon,Mar 31, 2008 | 3 PM | SC 507 | Michael Hopkins | Algebraic topology of topological field theories |  |
Mon,Mar 17, 2008 | 3 PM | SC 507 | Toshiyuki Kobayashi | Existence Problem of Compact Locally Symmetric Spaces |
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Mon,Mar 10, 2008 | 3 PM | SC 507 | Ben Weinkove | The Calabi-Yau equation | |
Mon,Mar 3, 2008 | 3 PM | SC 507 | Martin Nowak | Evolutionary Dynamics |
Fall 2007
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Oct 1, 2007 | 3:30 PM (a one time shift) | SC 507 | Clifford Taubes | Smooth Manifolds in Dimension 4 |  |
Mon,Oct 15, 2007 | 3 PM | SC 507 | Richard Taylor | Shimura Varieties and Rapoport-Zink Spaces |
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Mon,Oct 22, 2007 | 3 PM | SC 507 | Joe Harris | Uniformity of Rational Points on Curves |  |
Mon,Oct 29, 2007 | 3 PM | SC 507 | Slava Krushkal | The chromatic polynomial, the golden ratio, and quantum topology |
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Mon,Nov 5, 2007 | 3 PM | SC 507 | Dick Gross | On the parameters of discrete series |  |
Mon,Nov 19, 2007 | 3 PM | SC 507 | Paul Seidel (MIT) | Pairs of Pants |
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Mon,Dec 3, 2007 | 3 PM | SC 507 | Danijela Damjanovic | Stability of some Abelian actions |  |
Mon,Dec 10, 2007 | 3 PM | SC 507 | Mark Behrens (MIT) | Stable homotopy groups of spheres and modular forms |
Spring 2007
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,Feb 5, 2007 | 3 PM | SC 507 | Arthur Jaffe | Quantization and Renormalization | |
Mon,Feb 12, 2007 | 3 PM | SC 507 | Curt McMullen | Thermodynamics, dimension and moduli of Riemann surfaces |
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Mon,Feb 26, 2007 | 3 PM | SC 507 | Noam Elkies | Belyi functions | |
Mon,Mar 5, 2007 | 3 PM | SC 507 | Gerald Sacks | Differentially closed fields |
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Mon,Mar 12, 2007 | 3 PM | SC 507 | David Kazhdan | Poisson summation formula and its applications to the representation theory | |
Mon,Mar 19, 2007 | 3 PM | SC 507 | John Duncan | Vertex algebra and elliptic genera |
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Mon,Apr 2, 2007 | 3 PM | SC 507 | Dan Stroock | Most of DeGiorgi-Moser-Nash was already in Nash | |
Mon,Apr 9, 2007 | 3 PM | SC 507 | Barry Mazur | Transcendence conjectures about units in algebraic number fields and deformation problems |
Fall 2006
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,,Oct 2, 2006 | 3 PM | SC 507 | Cliff Taubes | Does Dirac have a tin ear? | |
Mon,Oct 16, 2006 | 3 PM | SC 507 | Peter Kronheimer | Three-manifolds, four-manifolds and Floer homology |
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Mon,Oct 23, 2006 | 3 PM | SC 507 | Ben Weinkove | Moment maps and geometry | |
Mon,Oct 30, 2006 | 3 PM | SC 507 | Shlomo Sternberg | The Ehrhart function for symbols and a generalization of Euler's constant |
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Mon,Nov 6, 2006 | 3 PM | SC 507 | Joseph Harris | Progress on algebraic curves |  |
Mon,Nov 13, 2006 | 3 PM | SC 507 | Samit Dasgupta | Conjectures on Hilbert's 12th Problem |
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Mon,Nov 20, 2006 | 3 PM | SC 507 | Shing-Tung Yau | Hermitian metrics on complex manifolds and vector bundles | |
Mon,Nov 27, 2006 | 3 PM | SC 507 | Horng-Tzer Yau | Brownian motion in quantum mechanics |
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Mon,Dec 4 | 3 PM | SC 507 | David Helm | Reduction of Shimura varieties and the Langlands program | |
Mon,Dec 11 | 3 PM | SC 507 | Lauren Williams | From total positivity on the Grassmannian to the asymmetric exclusion process |
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Mon,Dec 18, 2006 | 3 PM | SC 507 | Benedict Gross | Binary cubic forms and ternary quadratic forms: classifying the orbits of some group actions |
Spring 2006
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,,Feb 6, 2006 | 3 PM | SC 507 | Barry Mazur | Functional Equations, signs, and their implications [PDF] | |
Mon,,Feb 13, 2006 | 3 PM | SC 507 | Benedikt Gross | Arithmetic on elliptic curves: an update on Tate's Inventiones paper |
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Mon,,Mar 6, 2006 | 3 PM | SC 507 | Gerald Sacks | Vaught's Conjecture | |
Mon,,Mar 13, 2006 | 3 PM | SC 507 | Wilfried Schmid | Automorphic distributions and L-functions |
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Mon,,Apr 10, 2006 | 3 PM | SC 507 | Martin Nowak | Five rules for the evolution of cooperation | |
Mon,,Apr 24, 2006 | 3 PM | SC 507 | Richard Taylor | Elliptic curves and L-functions |
Fall 2005
| Date | Time | Room | Speaker | Title | Date | Time | Room | Speaker | Title | ||
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Mon,,Sep 26, 2005 | 3 PM | SC 507 | Curt McMullen | Renormalization | |
Mon,,Oct 3, 2005 | 3 PM | SC 507 | Mike Hopkins | Homotopy groups |
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Mon,,Oct 17, 2005 | 3 PM | SC 507 | Joe Harris | The Brill-Noether theorem: representation theory for curves | |
Mon,,Oct 24, 2005 | 3 PM | SC 507 | Dennis Gaitsgory | Affine Kac-Moody algebras and their representations |
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Mon,,Oct 31, 2005 | 3 PM | SC 507 | Yum-Tong Siu | Multiplier ideals -- a new technique linking analysis and algebraic geometry | |
Mon,,Nov 21, 2005 | 3 PM | SC 507 | S.-T. Yau | Mathematical problems in general relativity |
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Mon,,Dec 12, 2005 | 3 pm | SC 507 | Horng-Tzer Yau | Mathematical problems in quantum physics |