Work of Mark Shusterman and myself has proven an analogue of
Chowla's conjecture for polynomial rings over finite fields, which
controls k-points correlations of the Möbius function for k bounded
by a certain function of the finite field size...
Persistence modules and barcodes are used in symplectic topology
to define new invariants of Hamiltonian diffeomorphisms, however
methods that explicitly calculate these barcodes are often unclear.
In this talk I will define one such invariant...
The ellipsoidal embedding function of a symplectic four manifold
M measures how much the symplectic form on M must be dilated in
order for it to admit an embedded ellipsoid of some eccentricity.
It generalizes the Gromov width and ball packing...
The spectral norm provides a lower bound to the Hofer norm. It
is thus natural to ask whether the diameter of the spectral norm is
finite or not. During this short talk, I will give a sketch of the
proof that, in the case of Liouville domains, the...
In this talk, I will discuss a proof of a quantitative version
of the inverse theorem for Gowers uniformity norms 𝖴5 and 𝖴6 in
𝔽n2. The proof starts from an earlier partial result of Gowers and
myself which reduces the inverse problem to a study of...
A theorem by Kazhdan and Ziegler says that any property of
homogeneous polynomials---of a fixed degree but in an arbitrary
number of variables---that is preserved under linear maps is either
satisfied by all polynomials or else implies a uniform...
This is joint work with Haolin Shi (Yale). 3-webs are bipartite,
trivalent, planar graphs. They were defined and studied by
Kuperberg who showed that they correspond to invariant functions in
tensor products of SL_3-representations. Webs and...
Ellenberg and Gijswijt drastically improved the best known upper
asymptotic bound for the cardinality of a cap set in 2016. Tao
introduced the notion of slice rank for tensors and showed that the
Ellenberg-Gijswijt proof can be nicely formulated...
Let V be a complex vector space and consider symmetric d-linear
forms on V, i.e., linear maps Symd(V)→>C. When V is finite
dimensional and d>2, the structure of such forms is very
complicated. Somewhat surprisingly, when V has countably
infinite...
Several equivalent definitions of rank for matrices yield
non-equivalent definitions of rank when generalized to higher order
tensors. Understanding the interplay between these different
definitions is related to important questions in additive...
