2005-06 Geometry seminar
Fridays, Milner 216 at 4pm

Generally the speaker will give a 50-60 minute
talk, followed by a break, followed by more for
those who are interested.


Fall 2005 Geometry seminar

Sept. 9  D. Mortari (TAMU Aerospace)
Title: On a Family of Real Curves Arising from Satellite Placement
Click here for Abstract

Sept. 16 Z. Nie (TAMU)
Title: Karoubi's construction for motivic cohomology operations
Abstract: We use an analogue of Karoubi's construction for the topological reduced power operations in the motivic situation to give some cohomology operations in motivic cohomology. We prove many properties of these operations, and we show that they coincide, up to some nonzero constants, with the reduced power operations in motivic cohomology originally constructed by Voevodsky. The relation of our construction to Voevodsky's is, roughly speaking, that of a fixed point set to its associated homotopy fixed point set.

Sept. 23  E. Mezzetti (U. Trieste)  Moved to 3pm to avoid Frontiers conflict
Title: Congruences of lines and  systems of conservation laws.
Abstract: S.Agafonov and E.Ferapontov have introduced a construction  that allows one to associate naturally to every system of partial differential equations of conservation laws a congruence of lines in
an appropriate projective space. In particular, to hyperbolic systems  of Temple type, there correspond congruences of lines that form a planar pencil of lines. The language of Algebraic Geometry turns out to be
very natural in the study of these systems. In the talk, after recalling the definition and the basic facts on congruences of lines, I will illustrate the Agafonov-Ferapontov construction and some
results of classification for the Temple systems.

Sept. 30 go to Texas Geometry and Topology conference in Austin

Oct 7  A. Bernardi (U. Milano and TAMU)
Title: Secant varieties and the Big Waring problem

Oct. 14 M. Harada (U. Toronto)
Title: The topology of symplectic and hyperkahler quotients
Abstract: Symplectic and hyperkahler geometry lie at the crossroads of many exciting areas of research due to their relations to geometric representation theory, combinatorics, and certain areas of physics such as string theory and mirror symmetry. As often happens inmathematics, the presence of symmetry in these geometric structures --in this context, a   Hamiltonian G-action  for G a Lie group --turns out to be crucial in the computation of topological invariants, such as the Betti numbers or the cohomology ring, of symplectic and hyperkahler manifolds. I will give a bird's-eye, motivating overviewof the subject and then give a survey of my recent results on the topic.

Oct. 18 S. Wang (KIAS)  Note special day (Tues, 3pm)
Title: Legendrian surfaces in pseudoconformal geometry

Abstract: We introduce a pseudoconformal invariant functional
for Legendrian submanifolds in a sphere. Some aspects
of the critical submanifolds including some examples
in dimension 2 will be discussed.

Oct. 21 I. Coskun (MIT)
Title: The geometry of the moduli spaces of stable maps

Abstract: In the last decade the Kontsevich moduli spaces of stable maps have emerged as an invaluable tool for answering questions of algebraic geometry, mathematical physics and combinatorics. In this talk I will discuss recent work with Joe Harris and Jason Starr about the divisor theory of the Kontsevich moduli spaces. In particular, I will survey our knowledge of the ample cone and the effective cone of divisors.  If time permits, I will discuss some applications to questions of rational connectivity and possible perspectives our work offers on questions about divisors on moduli spaces of curves.


Oct. 28 D. Krashen (Yale)
Title: Zero cycles on homogeneous varieties

Note: Nov 3-5 there is a
star studded confence on groups and dynamical systems here at TAMU

Fri. Nov. 4  4pm O. Radko (UCLA)
Title: Morita equivalence of Poisson manifolds
Abstract: We will start with a brief introduction to Poisson manifolds. The earliest examples of Poisson manifolds arose as quotients of symplectic manifolds by symmetry groups. In fact, one of the fundamental discoveries in Poisson geometry (due to Alan Weinstein) is that any (integrable) Poisson manifold arises in this way, if groups are replaced by groupoids.
   The groupoid approach also naturally leads to an analogy between Poisson manifolds and algebras. This allows one to define Poisson analogs of modules, bimodules and Morita equivalence. We will discuss examples and computations of the Poisson manifold analogs of the groups of outer automorphisms of an algebra and of the Picard group (the group of self-Morita equivalencies).



Tues (Note special day) 3pm Nov. 8 P. Buergisser  (U. Paderborn)
Title: The computational complexity of the Euler characteristic and the Hilbert polynomial
Abstract: We describe a new approach to the classification of the computational
complexity of discrete invariants of complex algebraic varieties. The topological
Euler characteristic, Betti numbers and the Hilbert polynomial are studied. On
the complexity side, an analogon of L. Valiant's counting complexity class
#P is important. For the proofs, some of the ideas and tools of intersectin
theory, enumerative geometry and Schubert calculus are relevant. The
completeness results obtained can be interpreted in both the Turing and the Blum-Shub-Smale model of computation (joint work with Felipe Cucker and Martin Lotz).

Nov. 11 no seminar (attend the Harvey-Polking fest in Houston!)

Nov. 18  no seminar (speaking at the Chern-fest in Guanajuato)

Nov. 25, no seminar - Thanksgiving

Wed. Nov. 30 (Note special day) Damiano Testa (Cornell) 2pm
Title: Spaces of rational curves on del Pezzo surfaces

Dec. 9 M. Harada (Toronto)