Calendar

will speak on:

The derived equivalences of K3 surfaces and the K3 categories of certain cubic fourfolds are known to be realizable as Hodge isometries, i.e. lattice isometries preserving Hodge structures. On the other hand, Hodge isometries are also known to appear when one factorizes a birational map between varieties and tracks the actions on the middle cohomologies. When does a Hodge isometry induced from the derived equivalence of K3 surfaces/categories arise from a birational map? This is the first of two related talks discussing this question. In this talk, I will exhibit such examples for general K3 surfaces of degree 12. As a corollary, I will introduce how the construction gives an interesting relation in the Grothendieck ring of algebraic varieties. This is joint work with Brendan Hassett.

via Zoom Video Conferencing: https://harvard.zoom.us/j/837429475

Work of Ernst Specker (1960), Simon Kochen and Ernst Specker (1967), and John Bell (1964) concerning the non-existence of a hidden-variables theory reproducing the predictions of Quantum Mechanics is reviewed.
Subsequently, a novel approach to Quantum Mechanics yielding – among other things – a solution of the measurement problem is outlined.

via Zoom Video Conferencing: https://harvard.zoom.us/j/779283357

In this talk I’ll discuss work in preparation on the unknottedness of asymptotically conical self shrinkers in R^3.

via Zoom Video Conferencing: if you would like to attend, please email spicard@math.harvard.edu

Global anomalies in gauge theories are detected by the exponentiated eta-invariant, which becomes a cobordism invariant when perturbative anomalies vanish. We analyse global anomalies in four distinct (but equally valid) versions of the Standard Model of particle physics by computing the appropriate cobordism groups. In two cases we find that there are no global anomalies beyond the Witten anomaly associated with the SU(2) factor, while in the other cases we show that there are no global anomalies at all. This uncovers a subtle interplay between local and global anomalies in closely related gauge theories. We will then discuss a more subtle version of this `anomaly interplay’ occurring in a U(2) gauge theory defined without a spin structure.

via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126

We introduce a class of UV-regularized two-body interactions for fermions in $\R^d$ and prove a Lieb-Robinson estimate for the dynamics of this class of many-body systems. As a step towards this result, we
also prove a propagation bound of Lieb-Robinson type for continuum one-particle Schr\“odinger operators. We apply the propagation bound to prove the existence of a strongly continuous infinite-volume dynamics on the CAR algebra.

via Zoom Video Conferencing: https://harvard.zoom.us/j/147308224

We give a construction of a pseudo-Anosov map of a surface starting from (and almost isomorphic to) a hyperbolic automorphism of an n-torus. The construction arises from a peano curve based on an invariant space-filling tree. This construction allows to confirm (for degree 3) a conjecture of Fried regarding stretch factors of pseudo-Anosov maps.

via Zoom Video Conferencing: https://harvard.zoom.us/j/972495373

The most puzzling aspect of the `strange metal’ behavior of correlated electron compounds is that the linear in temperature resistivity often extends down to low temperatures, lower than natural microscopic energy scales. We consider recently proposed deconfined critical points (or phases) in models of
electrons in large dimension lattices with random nearest-neighbor exchange interactions. The criticality is in the class of Sachdev-Ye-Kitaev models, and exhibits a time reparameterization soft mode representing quantum gravity in dual holographic theories. We compute the low temperature resistivity in a large $M$ limit of models with SU($M$) spin symmetry, and find that the dominant temperature dependence arises from this soft mode. The resistivity is linear in temperature down to zero temperature at the critical point, with a co-efficient universally proportional to the product of the residual resistivity and the co-efficient of the linear in temperature specific heat. We argue that the time reparameterization soft mode offers a promising and generic mechanism for resolving the strange metal puzzle.

via Zoom Video Conferencing: https://harvard.zoom.us/j/977347126