I will discuss questions pertaining to geometric unlikely
intersections and transcendence in the setting of torii in positive
characteristic. This is based on work in progress joint with Anup
Dixit, Philip Engel, and Ruofan Jiang.
Every o-minimal structure determines a collection of "tame" or
"definable" subsets of bbRn. We can then ask about the fragment of
complex geometry present in the structure: Which holomorphic
functions are definable, and which spaces are cut out by...
We present solutions to two problems on indefinite integral
ternary quadratic forms. The first, highlighted by Margulis in
1990, concerns the distribution of the ternary Markoff spectrum
associated with minima of forms. The second, initiated by...
In the theory of error-correcting codes, list decoding allows a
decoder to output a list of candidates when attempting to remove
noise from a corrupted input. The constructions and algorithms for
such list decodable codes has had numerous...
This talk, which is based on two joint works, one with Pedro
Salomão and Richard Siefring and another with Michael Hutchings and
Vinicius Ramos, revolves around the role that restrictions on the
knot types of periodic Reeb orbits imposed by the...
I will prove Gromov's conjecture that every 3-manifold of
positive scalar curvature contains a short closed geodesic. The
proof uses Min-Max theory of minimal surfaces and a combinatorial
version of mean curvature flow. Time permitting, I will...
Over the past 50 years, cryptographers have constructed a number
of surprising and important primitives like public-key encryption,
which allows strangers to communicate privately even if
eavesdroppers hear everything they say. However, there are...
The group of Hamiltonian diffeomorphisms , equipped with the
Hofer metric , is a central object in symplectic topology. A
landmark result by Polterovich and Shelukhin established the
profound geometric complexity of this group for surfaces and
their...
Kudla and Millson proved in the 80's that the generating series
of special cycles in orthogonal and unitary Shimura varieties are
modular forms and a well-established conjecture of Kudla asks about
extensions to toroidal compactifications. In this...
