In this talk I will introduce the idea of Floer homotopy theory
and show how it can be used to give lower bounds on degenerate
Lagrangian intersections, in the case of plumbings of cotangent
bundles along a submanifold. The strength of the invariant...
In this talk, we begin by recalling Arnold’s geometric
formulation of hydrodynamics and then extend this framework to a
broader class of Hamiltonian systems, incorporating various PDEs
arising in mathematical physics. This motivates the study of...
We consider the symplectic area functional, constrained to loops
of vanishing Hamiltonian mean value: It has the same critical
points as the Rabinowitz action functional, and can be used to
define a similar Floer homology. In contrast to RFH, it...
In this lecture, we establish the kinematic foundation of the
Geometric QCD theory by constructing the unique stable vacuum of
the loop equation. We demonstrate that the MM loop equation admits
a solution of the form $W[C] = W_{fluct}[C] \exp{-...
Consider a collection of forms of odd degree with rational
coefficients. Birch proved in 1957 that if the number of variables
is sufficiently large, then the forms must have a nontrivial
rational zero. The bounds resulting from Birch's proof...
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.
I will present and discuss new analytical solutions to high
eccentricity perturbed Keplerian orbits undergoing Kozai-Lidov
oscillations. In particular, I will show that the complex dynamics
of hierarchical few body stellar systems - can be reduced...
I will employ twistor string theory to construct a bulk dual of
N = 4 super Yang-Mills in the regime of weak 't Hooft coupling. I
will also discuss applications of this duality to the study of
scattering amplitudes, giant graviton correlators, and...
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...
