Recently Added

Modularity lifting theorems for non-regular symplectic representations

George Boxer
University of Chicago
November 7, 2017

Abstract:  We prove an ordinary modularity lifting theorem for certain non-regular 4-dimensional symplectic representations over totally real fields.  The argument uses both higher Hida theory and the Calegari-Geraghty version of the Taylor-Wiles method.  We also present some applications of these theorems to abelian surfaces.  (Joint work with F. Calegari, T. Gee, and V. Pilloni.) 

Functoriality and algebraic cycles

Kartik Prasanna
University of Michigan
November 6, 2017

Abstract:  I will discuss the following question:  is Langlands functoriality given by algebraic cycles?  After a survey of some examples of interest, the talk will focus mostly on one case, namely that of inner forms GL(2) over a totally real field.  In this case, we can show that functoriality is given by something close to an absolute Hodge cycle; moreover, there is some hope of doing even better. (Joint work with Atsushi Ichino.)

Time quasi-periodic gravity water waves in finite depth

Massimiliano Berti
International School for Advanced Studies
November 8, 2017
We prove the existence and the linear stability of Cantor families of small amplitude time quasi-periodic standing water waves solutions, namely periodic and even in the space variable $x$, of a bi-dimensional ocean with finite depth under the action of pure gravity. Such a result holds for all the values of the depth parameter in a set of asymptotically full measure. This is a small divisor problem.

Morse-Bott cohomology from homological perturbation

Zhengyi Zhou
University of California, Berkeley
November 6, 2017
Abstract: In this talk, I will give a new construction of the Morse-Bott cochain complex, where the underlying vector space is generated by the cohomology of the critical manifolds. This new construction has two nice features: (1) It requires the minimum amount of transversality. (2) The choices made in the construction do not depend on the moduli spaces. I will explain its relation to three other constructions in literature, namely Austin-Braam's push-pull construction, Fukaya's push-pull construction and the cascades construction.