Upcoming Seminars & Events

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May 1, 2017
2:30pm - 3:30pm
TBA - Afonso Bandeira

Please note different day and location (Monday, Fine 110.)

Speaker: Afonso Bandeira, NYU
Location:
Fine Hall 110
May 3, 2017
3:00pm - 4:00pm
Some geometric aspects of the Allen-Cahn equation

In this talk I will discuss both local and global properties of the Allen-Cahn equation in closed manifolds.

Speaker: Marco Guaraco , University of Chicago
Location:
Fine Hall 314
May 4, 2017
10:45am - 11:45am
TBA - Jingyu Zhao
Speaker: Jingyu Zhao , IAS
Location:
IAS Room S-101
May 4, 2017
12:30pm - 1:30pm
TBA - Jun Su
Speaker: Jun Su , Princeton University
Location:
Fine Hall 110
May 4, 2017
2:00pm - 3:30pm
TBA - Ilya Khayutin
Speaker: Ilya Khayutin , Princeton University
Location:
Jadwin Hall 111
May 4, 2017
3:00pm - 4:30pm
TBA - Maya Stein
Speaker: Maya Stein , U. Chile
Location:
Fine Hall 224
May 4, 2017
4:30pm - 5:30pm
TBA - John Pardon
Speaker: John Pardon, Princeton University
Location:
Fine Hall 314
May 4, 2017
4:30pm - 5:30pm
TBA - Jared Weinstein
Speaker: Jared Weinstein , Boston University
Location:
Fine Hall 214
May 4, 2017
4:30pm - 5:30pm
Traveling-standing water waves and their stability

We describe a computational framework for computing hybrid traveling-standing waves that return to a spatial translation of their initial conditions at a later time. We introduce two parameters to describe these waves, and explore bifurcations from pure traveling or pure standing waves to these more general solutions of the free-surface Euler equations.  Next, we combine Floquet theory in time and Bloch theory in space to study the stability of traveling-standing waves to harmonic and subharmonic perturbations. For the latter, we have developed new boundary integral methods for the spatially quasi-periodic Dirichlet-Neumann operator. While much is known about the spectral stability of pure traveling waves, this is the first study of general subharmonic perturbations of pure standing waves.  Our unified approach for traveling-standing waves simplifies the eigenvalue problem that arises in the pure traveling case as well.   We conclude with a discussion of general quasi-periodic solutions of the free-surface Euler equations and present preliminary calculations of some simple cases.

Speaker: Jon Wilkening , UC Berkeley
Location:
Fine Hall 322
May 10, 2017
2:30pm - 3:30pm
TBA - Joe Zhong
Speaker: Joe Zhong, Princeton University
Location:
Fine Hall 224
May 11, 2017
10:45am - 11:45am
TBA - Manuel Rivera
Speaker: Manuel Rivera , University of Miami
Location:
IAS Room S-101
May 11, 2017
4:30pm - 5:30pm
TBA - Ananth Shankar
Speaker: Ananth Shankar , Harvard University
Location:
IAS Room S-101
May 18, 2017
4:30pm - 5:30pm
Potential automorphy of some non-self dual Galois representations

The IAS recently organized an Emerging Topics Working Group on " Applications to modularity of recent progress on the cohomology of Shimura varieties". Based on ideas of Calegari and Geraghty, and using recent results of Khare-Thorne and Caraiani-Scholze, the group (Allen, F.Calegari, Caraiani, Gee, Helm, Le Hung, Newton, Scholze, Thorne and myself) were able to prove modularity lifting theorems for n-dimensional Galois representations over CM (or totally real) fields without a (conjugate) self-duality hypothesis. Most notably our theorems apply in the `non-minimal' case. As applications we prove that elliptic curves over CM fields become modular after a finite base change. We also prove that cohomological (for trivial coefficients) automorphic forms on GL(2) over a CM field satisfy the Ramanujan conjecture. We are not able to reduce the Ramanujan conjecture to the Weil conjectures, rather we deduce it from the potentially automorphy of symmetric powers. 

Speaker: Richard Taylor , IAS
Location:
Fine Hall 214
May 29, 2017
9:00am - 5:00pm
Princeton-Rider Workshop On the Homotopy Theory of Polyhedral Products

Cartesian products have embedded within them certain natural subsets which are indexed by combinatorial information. The geometric characterization of these subspaces, known now as polyhedral products, has  application in toric geometry and topology, combinatorics, geometric group theory, number theory, homotopy theory and arachnid mechanisms. The workshop will focus on the topology and geometry of these and related spaces.

Speaker: Various,
Location:
Jadwin Hall A10