For Pauli stabilizer codes—such as surface codes and color
codes—transversal logical gates are strongly constrained by the
Bravyi–König bound. In particular, implementing a non-Clifford gate
transversally (as required for universality) demands three...
The group of Hamiltonian diffeomorphisms , equipped with the
Hofer metric , is a central object in symplectic topology. A
landmark result by Polterovich and Shelukhin established the
profound geometric complexity of this group for surfaces and
their...
Kudla and Millson proved in the 80's that the generating series
of special cycles in orthogonal and unitary Shimura varieties are
modular forms and a well-established conjecture of Kudla asks about
extensions to toroidal compactifications. In this...
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...
Among many things, dark matter could be made of new fundamental
or composite particles, which may feebly interact with nuclei or
electrons (“baryons”), as well as with themselves. Cosmological
observables are a promising avenue to test such...
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...
