Calendar

I will discuss recent developments at a new scientific interface between quantum optics, quantum many-body physics, information science and engineering. Specifically, I will focus on two examples at this interface involving realization of programmable quantum systems and their first scientific applications. In the first example, I will describe the recent advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Recent progress involving programmable quantum simulations with over 200 qubits in two-dimensional arrays, the exploration of exotic many-body phenomena, as well as realization and testing of quantum optimization algorithms will be discussed. In the second example, I will discuss progress towards realization of quantum repeaters for long-distance quantum communication. Specifically, I will describe experimental realization of memory-enhanced quantum communication, which utilizes a solid-state spin memory integrated in a nanophotonic diamond resonator to implement asynchronous Bell-state measurements. Prospects for scaling up these techniques, including realization of larger quantum processors and quantum networks, as well as their novel applications will be discussed.

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

Title: Recent progress on random field Ising model

Abstract: Random field Ising model is a canonical example to study the effect of disorder on long range order. In 70’s, Imry-Ma predicted that in the presence of weak disorder, the long-range order persists at low temperatures in three dimensions and above but disappears in two dimensions. In this talk, I will review mathematical development surrounding this prediction, and I will focus on recent progress on exponential decay and on correlation length in two dimensions. The talk is based on a joint work with Jiaming Xia and a joint work with Mateo Wirth.

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We introduce a derived version of Lie algebras in characteric p and describe two recent applications: first, we use them to classify infinitesimal deformations, generalising the Lurie-Pridham theorem in characteristic zero; second, we prove a Galois correspondence for purely inseparable field extension, extending work of Jacobson at height one. This talk is based on joint works with Mathew and Waldron.

Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09

In this talk, I will discuss some structural results for the cohomology of the moduli of semi-stable SL_n Higgs bundles on a curve. One consequence is a new proof of the Hausel-Thaddeus conjecture proven previously by Groechenig-Wyss-Ziegler via p-adic integration. If time permits, we will also discuss the case where the rank of the Higgs bundle is not coprime to the degree, so that the moduli spaces are singular due to the presence of the strictly semi-stable loci. We will explain that how intersection cohomology comes into play naturally. Based on joint work with Davesh Maulik.

Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening.  In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N.  Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations.  I will also discuss how these degeneracies provide a physical picture of confinement in 2d QCD with just a massless adjoint fermion.  This talk is based on joint work with R. Dempsey and I. Klebanov.

Zoom: https://harvard.zoom.us/j/977347126

Following work of Gross-Wallach, Gan-Gross-Savin defined what are called “modular forms” on the split exceptional group G_2.  These are a special class of automorphic forms on G_2.   I’ll review their definition, and give an update about what is known about them.  Results include a construction of cuspidal modular forms with all algebraic Fourier coefficients, and the exact functional equation of the completed standard L-function of certain cusp forms.  The results on L-functions are joint with Fatma Cicek, Giuliana Davidoff, Sarah Dijols, Trajan Hammonds, and Manami Roy.

Zoom: https://harvard.zoom.us/j/99334398740

Password: The order of the permutation group on 9 elements.

The periodicity of certain functions has been a topic of study throughout the long history of mathematics. It was a topic of study for you in high school trigonometry, and perhaps again in college Fourier analysis!  In this talk, I will revisit some of the ideas related to periodicity and Fourier analysis, and explain some of their relationships to other topics in mathematics, such as group theory and number theory.   In particular, I hope to say something about the important role of *non-abelian* groups of periods in contemporary mathematics.

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Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.

Zoom: https://harvard.zoom.us/j/977347126

Let K be a complete and algebraically closed field, such as C or the p-adic field C_p, and let f\in K(z) be a rational function of degree d\geq 2. The map f is said to be hyperbolic if there is some metric on its Julia set with respect to which it is expanding. A celebrated 1983 theorem of Mane, Sad, and Sullivan shows that for K=C, hyperbolic maps are J-stable, meaning that nearby maps in moduli space have topologically conjugate dynamics on their Julia sets. In this talk, we show that if K is non-archimedean, an a priori weaker bounded-contraction condition also yields J-stability. This project is joint work with Junghun Lee.

Go to http://people.math.harvard.edu/~demarco/AlgebraicDynamics/ for Zoom information.