Junior Geometry seminar

We meet on Tuesdays at 3:30 in RLM 9.166.

List of talks (2012, 2011).

Papers

Algebraic geometry

J-P. Serre, Géométrie algébrique et géométrie analytique.
A. Grothendieck, On the de Rham cohomology of algebraic varieties.
P. Deligne, Theorié de Hodge I, ICM1970.
P. Deligne, Theorié de Hodge II.
C. Voisin, Hodge theory and complex algebraic geometry.
A. Beilinson, Coherent sheaves on Pⁿ and problems in linear algebra.
D. Kaledin, Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie.
D. Kaledin, Cartier isomorphism and Hodge Theory in the non-commutative case.
J. Lurie, Tannaka duality for geometric stacks.
J. Lurie, E_k-algebras.
R. MacPherson, Intersection Homology and Perverse Sheaves.
B. Toën, Stacks and non-abelian cohomology.

Deformation theory

B. Fantechi, L. Goettsche, Elementary deformation theory, FGA explained.
J. Lurie, Moduli problems for ring spectra.
V. Drinfeld, C. Simpson, B-structures on G-bundles and local triviality.

Hitchin system in relation to Geometric Langlands

T. Hausel, M. Thaddeus, Mirror symmetry, Langlands duality, and the Hitchin system.
R. Donagi, T. Pantev, Langlands duality for Hitchin systems.
E. Frenkel, Lectures on the Langlands program and conformal field theory.

Geometric representation theory

D. Kazhdan, G. Lusztig, Schubert Varieties and Poincaré Duality.
G. Lusztig, Intersection Cohomology Methods in Representation Theory, ICM1990.
V. Deodhar, A Brief Survey of Kazhdan-Lusztig Theory and Related Topics.
H. Nakajima, Quiver varieties and Kac-Moody algebras.
H. Nakajima, Geometric construction of representations of affine algebras, ICM2002.
M. Brion, Lectures on the geometry of flag varieties.
M. Kashiwara, Y. Saito, Geometric Construction of Crystal Bases.
P. Etingof, Lectures on Calogero-Moser systems.
A. Okounkov, Random partitions and instanton counting, ICM2006.
N. Chriss, V. Ginzburg, Representation theory and complex geometry.
V. Drinfeld, Quantum groups, ICM1986.

Geometric topology

M. Atiyah, R. Bott, The Yang-Mills equations over Riemann surfaces.
J. Cheeger, J. Simons, Differential characters and geometric invariants.
M. Gromov, Pseudoholomorphic curves in symplectic manifolds.
S-T. Yau, On the Ricci curvature of a compact Kahler manifold and the complex Monge-Ampere equation I.

Mathematical physics

E. Witten, Supersymmetry and Morse theory.
E. Witten, Quantum field theory and the Jones polynomial.
E. Witten, Elliptic genera and quantum field theory.
E. Witten, The index of the Dirac operator in loop space.
R. Dijkgraaf, E. Witten, Topological gauge theories and group cohomologies.
E. Witten, Quantum field theory, Grassmannians, and algebraic curves.
M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function.
M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces.
K. Costello, Topological conformal field theories and Calabi-Yau categories.
K. Costello, A geometric construction of the Witten genus I.
P. Kronheimer, T. Mrowka, The genus of embedded surfaces in the projective plane.

Homotopy theory

S. Galatius, I. Madsen, U. Tillmann, M. Weiss, The homotopy type of the cobordism category.
M. Ando, A. Blumberg, D. Gepner, Twists of K-theory and TMF.
M. Atiyah, G. Segal, Equivariand K-theory and completion.
J. Adams, M. Atiyah, K-theory and the Hopf invariant.
G. Carlsson, Equivariant Stable Homotopy and Segal's Burnside Ring Conjecture.
D. Ravenel, Nilpotence and periodicity in stable homotopy theory.
J. Milnor, On manifolds homeomorphic to the 7-sphere.