Algebraic cycles are linear combinations of algebraic subvarieties
of an algebraic variety. We want to know whether all algebraic
subvarieties can be built from finitely many, in a suitable sense.
We present some recent results and counterexamples.
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...
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...
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 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...
We construct publicly verifiable non-interactive arguments that can
be used to delegate polynomial time computations. These
computationally sound proof systems are completely non-interactive
in the common reference string model. The verifier’s...
A Cartwright-Steger surface is a complex ball quotient by a certain
arithmetic cocompact group associated to the cyclotomic field
$Q(e^{2\pi i/12})$, its numerical invariants are with $c_1^2 = 3c_2
= 9, p_g = q = 1$. It is a cyclic degree 3 cover of...
In this talk I will present some joint work with Jeff Achter
concerning the problem of determining when the cohomology of a
smooth projective variety over the rational numbers can be modeled
by an abelian variety. The primary motivation is a...
We prove a parallel repetition theorem for general games with value
tending to 0. Previously Dinur and Steurer proved such a theorem
for the special case of projection games. Our proofs also extend to
the high value regime (value close to 1) and...
A famous result of Borel says that the cohomology of $\mathcal A_g$
stabilizes. This was generalized to the Satake compactification by
Charney and Lee. In this talk we will discuss whether the result
can also be extended to toroidal...
