Previous Conferences & Workshops
Markoff surfaces and strong approximation
Markoff triples are integer solutions of the equation
$x^2+y^2+z^2 = 3xyz$ which arose in Markoff's spectacular and
fundamental work (1879) on diophantine approximation and has been
henceforth ubiquitous in a tremendous variety of different
fields...
Diophantine analysis in thin orbits
We will explain how the circle method can be used in the setting
of thin orbits, by sketching the proof (joint with Bourgain) of the
asymptotic local-global principle for Apollonian circle packings.
We will mention extensions of this method due to...
From counting Markoff triples to Apollonian packings; a path via elliptic K3 surfaces and their ample cones
Arthur Baragar
4:30pm|Fine 214, Princeton University
The number of integer Markoff triples below a given bound has a
nice asymptotic formula with an exponent of growth of 2. The
exponent of growth for the Markoff-Hurwitz equations, on the other
hand, is in general not an integer. Certain elliptic K3...
Spectral gaps without frustration
Marius Lemm
In spin systems, the existence of a spectral gap has
far-reaching consequences. So-called "frustration-free" spin
systems form a subclass that is special enough to make the spectral
gap problem amenable and, at the same time, broad enough to
include...
Automorphy for coherent cohomology of Shimura varieties
Jun Su
We consider the coherent cohomology of toroidal
compactifications of Shimura varieties with coefficients in the
canonical extensions of automorphic vector bundles and show that
they can be computed as relative Lie algebra cohomology of
automorphic...
Motivic correlators and locally symmetric spaces IV
According to Langlands, pure motives are related to a certain
class of automorphic representations.Can one see mixed motives in
the automorphic set-up? For examples, can one see periods of mixed
motives in entirely automorphic terms? The goal of...
Short proofs are hard to find (joint work w/ Toni Pitassi and Hao Wei)
Ian Mertz
Proof complexity studies the problem computer scientists and
mathematicians face every day: given a statement, how can we prove
it? A natural and well-studied question in proof complexity is to
find upper and lower bounds on the length of the...
Torsion for abelian varieties of type III and new cases of the Mumford-Tate conjecture
Victoria Cantoral Farfan
4:30pm|Fine 314, Princeton University
Let $A$ be an abelian variety over a number field $K$. The
number of torsion points defined over a finite extension $L$ is
bounded polynomially in terms of the degree $[L:K]$. We compute the
optimal exponent for this bound, in terms of the dimension...
Open Gromov-Witten theory of $(mathbb{CP}^1,mathbb{RP}^1)$ in all genera and Gromov-Witten Hurwitz correspondence
Amitai Zernik
In joint work with Buryak, Pandharipande and Tessler (in
preparation), we define equivariant stationary descendent integrals
on the moduli of stable maps from surfaces with boundary to
$(\mathbb{CP}^1,\mathbb{RP}^1)$. For stable maps of the disk...
