Endoscopy theory for symplectic and orthogonal similitude groups

Bin Xu
Member, School of Mathematics
January 29, 2015
The endoscopy theory provides a large class of examples of Langlands functoriality, and it also plays an important role in the classification of automorphic forms. The central part of this theory are some conjectural identities of Harish-Chandra characters between a reductive group and its endoscopic groups. Such identities are established in the real case by Shelstad, but they are still largely unknown in the p-adic case due to our limited knowledge of characters in this case.

Symplectic forms in algebraic geometry

Giulia Saccà
Member, School of Mathematics
January 30, 2015
Imposing the existence of a holomorphic symplectic form on a projective algebraic variety is a very strong condition. After describing various instances of this phenomenon (among which is the fact that so few examples are known!), I will focus on the specific topic of maps from projective varieties admitting a holomorphic symplectic form. Essentially, the only such maps are Lagrangian fibrations and birational contractions. I will motivate why one should care about these types of maps, and give many examples illustrating their rich geometry.

A Conversation with Pia de Jong

Pia de Jong, Columnist and Novelist
January 30, 2015
This special Friends Event will feature the novelist and
columnist Pia de Jong, who will be reading from her most recent
work and discussing her life as a writer in the United States.
Since moving to Princeton with her family in 2012, Pia de Jong
has written a popular weekly column for the leading Amsterdam
daily newspaper, NRC Handelsblad, about her life in the U.S.
In the literary tradition of European writers visiting America
that includes Alexis de Tocqueville, Isabella Bird, and Alistair

On monotonicity testing and boolean isoperimetric type theorems

Subhash Khot
New York University
February 2, 2015

We show a directed and robust analogue of a boolean isoperimetric type theorem of Talagrand. As an application, we give a monotonicity testing algorithm that makes $\tilde{O}(\sqrt{n}/\epsilon^2)$ non-adaptive queries to a function $f:\{0,1\}^n \mapsto \{0,1\}$, always accepts a monotone function and rejects a function that is $\epsilon$-far from being monotone with constant probability. Joint work with Dor Minzer and Muli Safra. The paper is available on ECCC: http://eccc.hpi-web.de/report/2015/011/

Dimension expanders via rank condensers

Michael Forbes
Member, School of Mathematics
February 3, 2015
Expander graphs are sparse graphs with good connectivity properties and they have become ubiquitous in theoretical computer science. Dimension expanders are a linear-algebraic variant where we ask for a constant number of linear maps that expand subspaces of a vector space (instead of subsets of vertices). After their definition 10 years ago by Barak, Impagliazzo, Shpilka and Wigderson there are now two constructions of constant-degree dimension expanders, both of which suggest dimension expanders are more complicated than expander graphs.

Moduli of degree 4 K3 surfaces revisited

Radu Laza
Stony Brook University; von Neumann Fellow, School of Mathematics
February 3, 2015
For low degree K3 surfaces there are several way of constructing and compactifying the moduli space (via period maps, via GIT, or via KSBA). In the case of degree 2 K3 surface, the relationship between various compactifications is well understood by work of Shah, Looijenga, and others. I will report on work in progress with K. O’Grady which aims to give similar complete description for degree 4 K3s.

On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups

Atsushi Ichino
Kyoto University
February 5, 2015
The formal degree conjecture relates the formal degree of an irreducible square-integrable representation of a reductive group over a local field to the special value of the adjoint gamma-factor of its L-parameter. We prove the formal degree conjecture for odd special orthogonal and metaplectic groups in the generic case, which combined with Arthur's work on the local Langlands correspondence implies the conjecture in full generality. This is joint work with Erez Lapid and Zhengyu Mao.