Striving to make contact with mathematics and to be consistent with
neuroanatomy at the same time, I propose an idealized picture of
the cerebral cortex consisting of a hierarchical network of brain
regions each further subdivided into...
In this talk I will discuss the Sunflower Lemma and similar lemmas
that prove (in various contexts) that a set/distribution can be
partitioned into a structured part and a "random-looking" part. I
will introduce communication complexity as a key...
The Information Bottleneck (IB) is an information theoretic
framework for optimal representation learning. It stems from the
problem of finding minimal sufficient statistics in supervised
learning, but has insightful implications for Deep Learning...
The geometric optics trace formula gives the singular support of
wave trace on a compact Riemannian manifold. In the case of of a
one dimensional singular manifold, that is a metric (or quantum)
graph, this formula is exact and yields a crystalline...
Symplectic geometry, and its close relative contact geometry,
are geometries closely tied to complex geometry, smooth topology,
and mathematical physics. The h-principle is a general method used
for construction of smooth geometric objects...
Human memory is a multi-staged phenomenon of extreme complexity,
which results in highly unpredictable behavior in real-life
situations. Psychologists developed classical paradigms for
studying memory in the lab, which produce easily
quantifiable...
The "nearest neighbor (NN) classifier" labels a new data
instance by taking a majority vote over the k most similar
instances seen in the past. With an appropriate setting of k, it is
capable of modeling arbitrary decision rules. Traditional...
In this talk, I'll discuss the role that Lie algebras play in
algebraic topology and motivate the development of a "homotopy
coherent" version of the theory. I'll also explain an
"equation-free" formulation of the classical theory of Lie
algebras...
Open Gromov-Witten (OGW) invariants should count
pseudoholomorphic maps from curves with boundary to a symplectic
manifold, with various constraints on boundary and interior marked
points. The presence of boundary poses an obstacle to invariance.
In...
