I'll talk about the o-minimal structures R_LN and R_{LN,exp}
where one has an effective form of the finiteness property of
o-minimality. Unlike the more classical structure of Pfaffian
function, R_{LN,exp} contains the period integrals for
aribtrary...
Ricci solitons, introduced by R. Hamilton in the mid-80s, are
self-similar solutions to the Ricci flow and natural
generalizations of Einstein manifolds. Shrinking Ricci solitons, in
particular, model Type I singularities of the Ricci flow
and...
Two vector spaces of the same finite dimension are related by a
linear isomorphism; that’s how the dimension is defined. Similarly,
two simple subalgebras over complex numbers that are closed under
conjugate transpose are related by a unitary...
In a seminal paper from 2011, Wilfried Schmid and Kari Vilonen
made a bold proposal that apparently intractable questions in the
representation theory of real reductive groups could be resolved
with the help of natural Hodge structures coming from...
It is believed that topologically ordered gapped local
Hamiltonians in 2+1d consisting of commuting terms may not realize
a chiral anyon theory. There is even a formula that expresses the
chiral central charge of the edge theory as an integral of...
The P vs. NP problem was formulated about 50 years ago, and was
chosen to be one of the seven Clay millenium problems 25 years ago.
In this period our understanding of the depth, breadth and impact
of the problem has changed dramatically. I plan to...
The Linear Ordering Principle (LOP) is a total search problem
that generalizes the task of finding the minimum element of a given
order to settings in which the order need not be total. Building on
this, Korten and Pitassi (FOCS 2024) introduced the...
We propose an extension of Yao's standard two-party
communication model, where Alice and Bob respectively hold
probability distributions p and q over inputs to a function f,
rather than singleton inputs. Their goal is to estimate E[f(x,y)]
to within...
In probability theory, universality is the phenomenon where
random processes converge to a common limit despite microscopic
differences. For instance, the random walk, under mild conditions,
converges to the same Brownian motion seen from afar...
