Schedule for Algebra Geometry and Physics

Schedule for
Algebra Geometry and Physics

Sept 30   2:50 pm
P-131
Justin Sawon, SUNY at Stony Brook.
Holomorphic symplectic manifolds and quantum invariants of three-manifolds

In (real) three-dimensional topology, Chern-Simons-Witten invariants can be constructed by applying a Lie algebra weight system to a universal quantum invariants. More recently a new weight system coming from holomorphic symplectic manifolds was discovered which gives the Rozansky-Witten invariants.
I will describe the above ideas and how holomorphic symplectic manifolds lead to a `Lie algebra object'. I may also describe a construction of the 3-dimensional TQFT associated to the Rozansky-Witten invariants, which is analogous to Reshetikhin and Turaev's construction of the Chern-Simons-Witten TQFT.

Oct 7   2:50 pm

No Meeting This Week.

Oct 14   2:50 pm
P-131
Mark Andrea de Cataldo, SUNY at Stony Brook.
The cohomology of algebraic varieties: motives

First in a short series of talks where I will discuss motives in the context of the cohomology of algebraic varieties. The last talk of the series will be devoted to a result of mine with Migliorini that makes these calculations quite concrete in many cases.

Oct 21   2:50 pm
P-131
Mark de Cataldo, SUNY at Stony Brook.
The cohomology of algebraic varieties: motives (part II)

Part II of the series.

Oct 28   2:50 pm
P-131
Mark Andrea de Cataldo, SUNY at Stony Brook.
The cohomology of algebraic varieties: motives (Part III)

Part three in the series. I will discuss my results with Migliorini on how to compute algebraic cycles on some configurations spaces.

Nov 4   2:50 pm
P-131
Peter Zograf, SUNY at Stony Brook.
2D Topological gravity and Weil-Petersson volumes of moduli spaces of curves

Nov 11   2:50 pm
P-131
Amy Ksir, SUNY at Stony Brook.
D-branes and algebraic surfaces

The first of two talks. I will attempt an introduction to D-branes and geometry, then describe the connections between a) Branes in type IIA string theory, b) Algebraic surfaces in M-theory, c) Seiberg-Witten integrable systems, and d) N=2 gauge theories.

Nov 18   2:50 pm
P-131
Samuel Grushevsky, Princeton University.
Effective algebraic Schottky problem

We present a method of obtaining a solution to the Schottky problem algebraic in terms of theta constants: we show that the degree of the Jacobian locus is equal to the volume of the moduli space of curves in some metric, obtain an upper bound on this volume, and then use this upper bound to effectively obtain algebraic equations for theta constants starting from the KP partial differential equation

Nov 25   2:50 pm
P-131
Amy Ksir, SUNY at Stony Brook.
D-branes and algebraic surfaces (part II)

The second of two talks. I will present recent results of mine with Stephen Naculich, and related work by Argyres et al, on elliptic surfaces and type IIA configurations with two negatively-charged orientifold sixplanes.

Dec 2   2:50 pm
P-131
Blaine Lawson, SUNY at Stony Brook.
Boundaries of varieties in projective manifolds

Dec 9   2:50 pm
P-131
Blaine Lawson, SUNY at Stony Brook.
Projective hulls and the projective Gelfand transformation

Sept 30 2:50 pm P-131	Justin Sawon, SUNY at Stony Brook. Holomorphic symplectic manifolds and quantum invariants of three-manifolds In (real) three-dimensional topology, Chern-Simons-Witten invariants can be constructed by applying a Lie algebra weight system to a universal quantum invariants. More recently a new weight system coming from holomorphic symplectic manifolds was discovered which gives the Rozansky-Witten invariants. I will describe the above ideas and how holomorphic symplectic manifolds lead to a `Lie algebra object'. I may also describe a construction of the 3-dimensional TQFT associated to the Rozansky-Witten invariants, which is analogous to Reshetikhin and Turaev's construction of the Chern-Simons-Witten TQFT.

Oct 7 2:50 pm	No Meeting This Week.

Oct 14 2:50 pm P-131	Mark Andrea de Cataldo, SUNY at Stony Brook. The cohomology of algebraic varieties: motives First in a short series of talks where I will discuss motives in the context of the cohomology of algebraic varieties. The last talk of the series will be devoted to a result of mine with Migliorini that makes these calculations quite concrete in many cases.

Oct 21 2:50 pm P-131	Mark de Cataldo, SUNY at Stony Brook. The cohomology of algebraic varieties: motives (part II) Part II of the series.

Oct 28 2:50 pm P-131	Mark Andrea de Cataldo, SUNY at Stony Brook. The cohomology of algebraic varieties: motives (Part III) Part three in the series. I will discuss my results with Migliorini on how to compute algebraic cycles on some configurations spaces.

Nov 4 2:50 pm P-131	Peter Zograf, SUNY at Stony Brook. 2D Topological gravity and Weil-Petersson volumes of moduli spaces of curves

Nov 11 2:50 pm P-131	Amy Ksir, SUNY at Stony Brook. D-branes and algebraic surfaces The first of two talks. I will attempt an introduction to D-branes and geometry, then describe the connections between a) Branes in type IIA string theory, b) Algebraic surfaces in M-theory, c) Seiberg-Witten integrable systems, and d) N=2 gauge theories.

Nov 18 2:50 pm P-131	Samuel Grushevsky, Princeton University. Effective algebraic Schottky problem We present a method of obtaining a solution to the Schottky problem algebraic in terms of theta constants: we show that the degree of the Jacobian locus is equal to the volume of the moduli space of curves in some metric, obtain an upper bound on this volume, and then use this upper bound to effectively obtain algebraic equations for theta constants starting from the KP partial differential equation

Nov 25 2:50 pm P-131	Amy Ksir, SUNY at Stony Brook. D-branes and algebraic surfaces (part II) The second of two talks. I will present recent results of mine with Stephen Naculich, and related work by Argyres et al, on elliptic surfaces and type IIA configurations with two negatively-charged orientifold sixplanes.

Dec 2 2:50 pm P-131	Blaine Lawson, SUNY at Stony Brook. Boundaries of varieties in projective manifolds

Dec 9 2:50 pm P-131	Blaine Lawson, SUNY at Stony Brook. Projective hulls and the projective Gelfand transformation