Past Events
Saraswathi Venkatesh: Poincare, energy hypersurfaces, and mirror symmetry
We discuss a problem in classical dynamics for which a standard approach yields no information. We then discuss how mirror symmetry prompts a modification of the standard toolbox, producing interesting…
The buzzword ‘modeling’ covers a multitude of sins, but in this hour I'll lift the veil on several episodes where I tried, clumsily, my style of modeling in applied mathematics—from noticing a surprising phenomenon to publishing an article. Unconventionally for a talk, more failures…
I shall describe two problems in optics, one in nonimaging lens design and one in visual optics, that are solved through appropriate caustic structures.
After discussing background on valuative criteria in algebraic geometry, I'll present the little-known valuative criterion for locally closed immersions. Time permitting, I'll discuss the following applications of this criterion:
1. The moduli stack of hyperelliptic genus g curves…
Let N be the total space of a bundle over some k-dimensional torus with fiber Z, where Z is a connected sum of sphere products. It turns out that N can be embedded into C^n and CP^n as a monotone Lagrangian submanifold. It is possible to construct embeddings of N with different minimal…
I will introduce enumerative invariants which count curves with local tangency constraints in a symplectic manifold. For closed manifolds, we give an algorithm which computes these invariants in terms of previously known blowup Gromov-Witten invariants. For open manifolds, these invariants can…
In 1985, Gromov helped revolutionize the field of symplectic topology by introducing J-holomorphic curves and proving certain compactness results regarding them. In this talk, we will give a brief introduction to the theory of J-holomorphic curves and look at a few of their many applications in…