The black hole information paradox — whether information escapes
an evaporating black hole or not — remains one of the greatest
unsolved mysteries of theoretical physics. The apparent conflict
between validity of semiclassical gravity at low...
Galaxy surveys, which observe the positions and shapes of
galaxies across large areas of the sky, can map a significant
fraction of our cosmic volume. With the recent or imminent start of
several next-generation projects — including LSST, Euclid...
In this talk we will describe the behaviors of flat surfaces and
geodesics on hyperbolic surfaces, as their genera tend to infinity.
We first discuss enumerative results that count the number of such
surfaces or geodesics (which can be viewed as...
Andras Juhasz has explained in his talk how machine learning was
used to discover a previously unknown relationship between
invariants in knot theory. This relationship is a connection
between a classical knot invariant (the signature) and a new...
In this talk, I will establish a sharp bound on the growth of
cuspidal Bianchi modular forms. By the Eichler-Shimura isomorphism,
we actually give a sharp bound of the second cohomology of a
hyperbolic three manifold (Bianchi manifold) with local...
The absorption method is a very simple yet surprisingly powerful
idea coming from extremal combinatorics which allows one to convert
asymptotic results into exact ones. It has produced a remarkable
number of success stories in recent years with...
Combinatorial Invariance: a Case Study of Pure Math /
Machine Learning Interaction
The combinatorial invariance conjecture is a fascinating
conjecture in Representation Theory. Basically it says that
certain important polynomials ("Kazhdan-Lusztig...
Recent B-meson data show a reinforced set of deviations from the
Standard Model predictions, pointing to violations of lepton flavor
universality. I will critically review these data and discuss their
theoretical interpretation, including their...
The signature of a knot K in the 3-sphere is a
classical invariant that gives a lower bound on the
genera of compact oriented surfaces in the 4-ball with
boundary K. We say that K is hyperbolic if its
complement admits a complete, finite volume...
