Physics inspired mathematics helps us understand the random
evolution of Markov processes. For example, the Kolmogorov forward
and backward differential equations that govern the dynamics of
Markov transition probabilities are analogous to the...
Most readers of Toni Morrison know her best as a novelist. She
is the author of 11 extraordinary works of fiction, including the
1987 masterpiece, Beloved, and her work is assigned
in high school and college classrooms and debated at book
club...
I will explain that incompressible Navier-Stokes is the wrong
equation to describe turbulence in low Mach number molecular fluids
because it neglects the effects of thermal noise. There should, in
fact, be strong effects of thermal noise throughout...
We present an elementary summary of known results, and open
questions, on scaling problems in hydrodynamic turbulence in three
dimensions. The goal is to provide some background for the two
talks to follow, and summarize Victor Yakhot's theory...
I will explain the construction of a functor from the exact
symplectic cobordism category to a totally ordered set, which
measures the complexity of the contact structure. Those invariants
are derived from a bi-Lie infinity formalism of the rational...
Let λλ be the Liouville function
and P(x)P(x) any polynomial that is not a square. An open
problem formulated by Chowla and others asks to show that the
sequence λ(P(n))λ(P(n)) changes sign infinitely often. We
present a solution to this problem for...
Motivated by a formal similarity between the Hard Lefschetz
theorem and the geometric Satake equivalence we study vector spaces
that are graded by a weight lattice and are endowed with linear
operators in simple root directions. We allow field...
In his seminal paper from 1973, Garland introduced a machinery
for proving vanishing of group cohomology for groups acting on
Bruhat-Tits buildings. This machinery, known today as “Garland’s
method”, had several applications as a tool for proving...
Reconstruction of bulk operators within the causal wedge is
simple to achieve using Lorentzian causal bulk dynamics. In
contrast, the only known methods for reconstructing arbitrary
operators in the full entanglement wedge (the Petz map,
modular...
