The regularity theory for the Navier-Stokes equation will be
reviewed. Motivations from Kolmogorov’s phenomenological theory of
turbulence will be discussed. Rigorous mathematical results are
obtained to confirm some of the phenomenologies.
I will discuss joint work with McLean and Smith, lifting the
results of Seidel, Lalonde, McDuff, and Polterovich concerning the
topology of Hamiltonian fibrations over the 2-sphere from rational
cohomology to complex cobordism. In addition to the...
We consider variational principles related to V. I. Arnold's
stability criteria for steady-state solutions of the
two-dimensional incompressible Euler equation. Our goal is to
investigate under which conditions the quadratic forms defined by
the...
As solutions can be efficiently verified, any NP-complete
problem can be solved by exhaustive search. Unfortunately, even for
small instances the running time for exhaustive search becomes very
high.
Legendrian torus knots were classified by Etnyre and Honda. I
will explain the classification of Legendrian torus links. In
particular, I will describe restrictions on the Legendrian torus
knots that can be realized as the components of a Legendrian...
Human learning outstrips modern machine learning and AI in at
least three abilities: rapid robust learning, in effectively open
worlds, in near-real time with very little energy. Mathematical
formalization of signature human abilities has the...
The topic of the talk will be Floer theories on exact symplectic
orbifolds with smooth contact boundary. More precisely, I will
first describe the construction, which only uses classical
transversality techniques, of a symplectic cohomology group
on...
In 1986, Hooley applied (what practically amounts to) the
general Langlands reciprocity (modularity) conjecture and GRH in a
fresh new way, over certain families of cubic 3-folds. This
eventually led to conditional near-optimal bounds for the
number...
Let f=∑anxn∈ℚ[x] be a power series which is also a meromorphic
function in some neighborhood of the origin. The subject of the
talk will be how certain conditions on f(x) as a meromorphic
function actually guarantee that f(x) is an algebraic...
