Supersymmetric quantum field theories (SQFTs) have been intensely researched by both physicists and mathematicians for decades. For physicists, they furnish computationally and conceptually tractable models from which one may hope to extract general lessons about quantum field theory. On the other hand, supersymmetry also often equips such theories with additional structures, both algebraic and geometric, which are mathematically rich and warrant study in their own right. This event focuses on SQFTs of diverse dimension, the geometry of their moduli spaces of vacua, and the algebras formed by their supersymmetrypreserving operators, particularly when these take the form of a vertex operator algebra. The interplay between these three subjects bears fruit; a better understanding of any one of the three enriches both of the other two. This program offers an opportunity for both physicists and mathematicians working on all three subjects to meet and share ideas, techniques, and inspiration.
This program will also be hosting a workshop: Symplectic Singularities, Supersymmetric QFT, and Geometric Representation Theory March 31st – April 4, 2025.
More information to come in Fall 2024.
]]>Modern curvecounting theories were in part inspired by the work of physicists yet have active lives of their own as interesting and rich mathematical notions with connections to many areas of mathematics. A plethora of enumerative invariants have been developed, including Gromov–Witten (GW) invariants, GLSM invariants, Fan–Jarvis–Ruan–Witten (FJRW) invariants, as well as variants of these curvecounting theories. Many conjectures about enumerative invariants have arisen from physics, providing both deep insight as well as strategies for effective computation. Several of these conjectures have been proven in recent years, sometimes in their original form, and other times after the conjecture has been translated into a mathematically more natural framework. This program will focus on the higher genus curve counts from multiple angles, including geometric, computational and categorical perspectives.
On the geometric side, the program will investigate various moduli spaces recently introduced as tools to understand higher genus invariants, including (but not limited to) desingularizations of moduli of stable maps, moduli of MixedSpinP fields, and logarithmic gauged linear sigma models, as well as recent progress on skeinvalued invariant counts of higher genus holomorphic curves with Lagrangian boundary conditions in CalabiYau threefolds and higher genus open BPS invariants.
On the computational side, higher genus GW invariants of Calabi–Yau threefolds are expected to satisfy universal properties such as Yamaguchi–Yau finite generation, the BCOV holomorphic anomaly equations, and the Castelnuovo bound, which have been established for quintic Calabi–Yau threefolds. Progress and difficulties in generalizing these results to other Calabi–Yau threefolds, and to more general targets, will be investigated during the program, with the participation of physicists for synergistic effect. Building on these results and other developments, the g=2 Gromov–Witten invariants of the quintic have been rigorously determined. There is much room and hope for further exciting progress, as physicists have a prediction for the Gromov–Witten invariants of the quintic up to genus 64.
Most of the above enumerative invariants are expected to agree with the corresponding enumerative categorical invariants constructed by Caldararu–Tu: the Fukaya category of a symplectic manifold for GW theory; the wrapped Fukaya category of a symplectic LandauGinzburg model for FJRW theory; the derived category of a Calabi–Yau manifold for BCOV theory; the category of matrix factorizations for Bmodel FJRW theory. From this point of view, categorical/homological mirror symmetry (which can be viewed as a version of genuszero open mirror symmetry) implies enumerative mirror symmetry for all genera. The main challenge lies in identifying categorical invariants with geometric ones, which is one of the main themes of this program.
This program will also be hosting a workshop: Recent developments in higher genus curve counting: February 1014, 2025
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In recent years, new probabilistic methods were developed to offer a rigorous approach to constructing Euclidean path integral measures for several interacting quantum field theories, including the Liouville theory in d=2 and the φ4 theory in d=3. Another rigorous approach explores the BPS/CFT correspondence, relating the nonperturbative physics of supersymmetric gauge theories in four dimensions to conformal blocks of some d=2 CFTs and their integrable FT analogues. For example, Alday, Gaiotto and Tachikawa connected the d=2 Liouville theory to the A1type Sclass N=2 supersymmetric theories in d=4. On the gauge theory side, Nekrasov partition functions provide combinatorial expressions for Liouville conformal blocks. On the probabilistic side, Kupiainen, Rhodes and Vargas applied rigorous methods to the derivation of the DOZZ formula for the 3point function of Liouville theory, which is a oneloop approximation on the d=4 side. Extension to full conformal bootstrap for vertex operator correlation functions and conformal blocks was achieved in subsequent work of those authors together with Guillarmou. The emergence of the combinatorics of gauge theory predicted by Nekrasov remains a challenge. The approach to Liouville theory proposed by Sheffield gives yet another combinatorial perspective, at least in the genus zero case. An approach based on integration by parts allowing to characterize Euclidean quantum field theories in d=2 with exponential interactions, much like the classical Liouville theory, has been recently put forward by De Vecchi, Gubinelli and Turra. Another interesting direction concerns imaginary versions of Liouville theory, which has been recently constructed via probabilistic methods in Guillarmou, Kupiainen, Rhodes, and their relations to minimal models, the minimal string and 3d gravity.
In d=3 new constructions of the φ4 theory were given using SPDE and stochastic quantisation approaches by Hairer, Gubinelli, Hofmanova, Barashkov and others. We will work to see if these rigorous approaches could be combined with the probabilistic bootstrap method to confront the vast number of results from numerical bootstrap in three and four dimensions. Likewise, it would be interesting to connect the probabilistic bootstrap to the form factor bootstrap method developed for the study of integrable QFTs.
The stochastic optimal control approach of Barashkov and Gubinelli is closely connected to Polchinski’s renormalisation group equation. Building on this, Bailleul, Chevyrev and Gubinelli defined, in any number of spacetime dimensions, a formally nonperturbative quantization method applicable also to gauge theories and independent of a pathintegral formulation, compatible with WilsonPolchinski equations whenever path integral formulations exist. Since string theory predicts the existence of nontrivial conformal field theories with no classical limit and no path integral formulation, this opens up a bridge between different arenas of research, once these probabilistic methods are extended to include tensor fields of higher rank.
There are a plethora of other topics we would like to address, such as finding stochastic analytic approaches to path integral Lefschetz thimbles and exploring them in the simplest cases of two dimensional sigma models, such as O(N) and CPN1. QFT practitioners would benefit from incorporating probabilistic methods, potentially extending them to the physically interesting domain: gauge theories in 3 ≤ d ≤4 dimensions.
There will be six minicourses giving introductions to regularity structure, stochastic quantization, RG and WilsonIto fields, combinatorics from nonperturbative gauge theory, probabilistic approaches to quantum Liouville theory, stochastic aspects of YangMills theory, and integrable quantum field theory.
MINI COURSE LECTURES
*dates and lecturers TBA
• Sayed Ali Akbar Ghorashi (Stony Brook University)
• Jennifer Cano (Stony Brook University
• Masatoshi Sato (Yukawa institute and Kyoto University)
• Titus Neupert (Zurich)
• Shinsei Ryu (Princeton)
Over the last few years there has been a new resurrection of nonHermitian physics across various fields in both classical and quantum physics, ranging from condensed matter, atomic and photonic systems, soft matter and stochastic models to highenergy and quantum field theories. One of the recent major developments in this area revolves around the topological and symmetry protected phase. It has been shown that many notions such the concept of the gap, nature of gapless structures and bulk boundary correspondence vary drastically from the Hermitian topological phases. Despite the developments in all these directions, a unified understanding of the interplay between these emergent notions is lacking.
Despite these developments, which stimulated much interest in both theoretical and experimental directions, there has been a lack of organized programs that bring experts in all related areas to generate a coherent community. In this program we plan to bring together experts from various backgrounds to ignite dialogues and collaborations across disciplines in order to address the following aspects of novel nonHermitian topological phases:
Theme 1: A complete understanding of the anomalous nature of the bulkboundary correspondence, often referred to as the “nonHermitian skin effect” is still lacking. Particularly, is there a general topological explanation for all skineffects? How much does topology dictate its presence or absence? What is the role of geometry of the underlying lattice model? Does the presence or absence of specific symmetries teach us anything about it?
Theme 2: In the realm of Hermitian physics, symmetries play an essential role. For example, symmetry can dictate the topological character of bands which led to the theory of topological quantum chemistry. What is the role of symmetry and its interplay with topology in nonHermitian systems? And to what extent the symmetry indicator formalisms can be applied to nonHermitian systems ?
Theme 3: Beyond the effective Hamiltonian formalism, a truly open quantum system is described via a Lindblad quantum master equation. However, the two approaches are not always consistent nor have the same power. What are the possible reconciliations?
Theme 4: Recent attempts in nonHermitian random matrix theory and critical phenomena call for a better understanding of how disorder, interaction and more generally correlation can affect nonHermitian physics?
Theme 5: The effective field theory of nonHermitian systems exposes the subtle interplay between nonHermiticity, topology, geometry and symmetry. For example, it is known that nonHermitian systems are very sensitive to the boundary conditions of the model. What field theoretical formulation can capture various boundary phenomena such as the skineffect?
This program and its accompanying workshop will bring together experts from theoretical (mostly) and experimental communities to understand various fundamental and practical issues related to the role of topology, geometry and symmetry in nonHermitian physics. Our goal is to address the topics above and catalyze interdisciplinary collaborations.
This program will also be hosting a workshop: NonHermitian topology, geometry and symmetry across physical platforms: September 2327, 2024
More information to come in Spring 2024.
]]>Organizing by:
This program in Mathematics is inspired by a circle of ideas originating in quantum field theory and string theory, particularly the study of the quantum field theories “of class S”. These field theories have been the subject of intense study in the high energy theory community over the last thirteen years. Many of the constructions from physics have now found their natural place in vibrant areas of research in pure mathematics. Physical insights have helped to catalyze the realization that the mathematics of flat surfaces, triangulated categories, cluster algebras, symplectic geometry, and ordinary differential equations have a common Rosetta stone, in the theory of meromorphic quadratic differentials on Riemann surfaces.
This program, partly motivated by physics, is structured around meromorphic quadratic differentials on Riemann surfaces, and their relations with stability conditions and enumerative invariants in geometry. We aim to bring these diverse mathematical communities together to focus on the core constructions of mutual interest, to see if techniques from one field can shed light on questions from another, and to make progress in each of the directions separately.
The focus in Week 1 and 2 will be on the geometry of the spaces parameterising quadratic differentials and stability conditions, and the interactions between them
WEEK 1: May 13 – 17, 2024
Minicourses:
Speaker: Fabian Haiden (Centre for Quantum Mathematics, Denmark)
Title: Introduction to stability conditions
Speaker: Anton Zorich* (University of Paris 7)
Title: Some basic facts about geometry and dynamics of moduli spaces of quadratic differentials
WEEK 2: May 20 – 24, 2024
Minicourse:
Speaker: Tom Bridgeland (University of Sheffield)
Title: Geometric structures on spaces of stability conditions induced by DonaldsonThomas invariants
WEEK 3: May 27 – 31, 2024
FOCUS: Spectral networks and BPS states
Minicourses:
Speaker: Pierrick Bousseau (University of Georgia)
Title: Scattering diagrams with a view toward spectral networks
Speaker: Andy Neitzke (Yale University)
Title: Introduction to spectral networks
WEEK 4: June 3 – 7, 2024
Workshop: Moduli of Meromorphic Quadratic Differentials devoted to all these topics
WEEK 5: June 10 – 14, 2024
Focus: Discussions and research talks
WEEK 6: June 17 – 21, 2024
Focus: Discussions, research and future outlook talks.
Organizing by:
This program will bring together physicists and mathematicians with expertise in different facets of particle scattering in planar N=4 superYangMills theory, in order to try to solve the theory for generic values of the coupling and kinematical variables.
It has been a longstanding quest to solve stronglyinteracting fourdimensional relativistic quantum field theories by analytical methods. N = 4 superYangMills theory (SYM) is the “hydrogen atom” of gauge theories. It is the archetype for the AdS/CFT correspondence, connecting it to string theory and gravity, particularly at strong coupling. Perturbatively, its gluon scattering amplitudes closely resemble those for the gauge theory of the strong interactions, quantum chromodynamics (QCD). Hence it has proven indispensable as a testing ground for powerful new computational methods for precision collider physics. In the planar limit of a large number of colors (gauge group SU(Nc) with Nc → ∞), N = 4 SYM is integrable, and its scattering amplitudes are dual to the expectation values of Wilson loops for closed lightlike polygons. The perturbative expansion of planar N = 4 SYM has remarkable geometric features, centered around polytopes related to various Grassmannians and the
differential forms that live on them.
There are currently three independent descriptions of scattering amplitudes in planar N = 4 SYM, illustrated in the figure.
A weakcoupling formulation makes contact with perturbative methods involving Feynman diagrams; a “holographic” strongcoupling formulation employs minimalarea surfaces in Antide Sitter space; and a pentagon operator product expansion (POPE) approach exploits the twodimensional integrability of a dual string picture at finite coupling in various kinematic limits. These formulations are all mutually consistent. (Indeed the compatibility of the POPE and perturbative approaches can be established through eight loop orders.) But they are formulated in mathematically very distinct ways, based on different underlying physical principles, and they make different properties of amplitudes manifest. In this program, the goal is to find a unified description of amplitudes in this theory that matches onto each of these formulations in the appropriate limit. Mathematically, the proposal is to search for functions that are able to interpolate between weak and strong coupling, for arbitrary kinematics, using all the knowledge we have about them in the respective limits. In this way one could gain a quantitative picture of how weak coupling excitations (gluons) evolve into strong coupling ones (strings) under a variety of physical circumstances. The spinoff for QCD could also be very important.
This program also has an associated workshop: Mathematical Aspects of N=4 SuperYangMills Theory: February 26March 1, 2024
MINI COURSE SCHEDULE
WEEK 1: January 8 – January 9, 2024
Monday 1/8/24: 1:30PM2:30PM – Seminar Room – 313
Tuesday 1/9/24: 10:30AM11:30AM Seminar Room – 313
Tuesday 1/9/24: 1:30PM2:30PM – Seminar Room – 313
Speaker: Lauren Williams
Title: The positive (tropical) Grassmannian, the amplituhedron, and cluster algebras
In this talk I will discuss the amplituhedron, focusing on the problem of finding tilings, as well as the connection to cluster algebras, such as the “cluster adjacency” phenomenon. I’ll start by describing what we know for the m=2 amplituhedron, including its connection to the positive tropical Grassmannian, and then I’ll describe the state of the art for m=4.
WEEK 1: January 10 – January 12, 2024
Wednesday 1/10/24: 10:30AM11:30AM – Seminar Room – 313
Thursday 1/11/24: 10:30AM11:30AM – Seminar Room – 313
Friday 1/12/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Clément Dupont
Title: Motivic coaction for periods and amplitudes
The motivic coaction is a general structure of the algebra of periods (integrals on algebraic varieties) which extends the classical Galois theory of algebraic numbers. In these lectures I will give an introduction to this formalism and illustrate it with examples arising in particle physics. In particular, I will explain how the techniques of twisted cohomology explain the existence of a ‘cosmic Galois theory’ for Feynman integrals in dimensional regularization.
WEEK 2: January 16 – January 18, 2024
Tuesday 1/16/24: 10:30AM11:30AM – Seminar Room – 313
Wednesday 1/17/24: 10:30AM11:30AM – Seminar Room – 313
Thursday 1/18/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Lionel Mason
Title: Strong Coupling and Minimal Surfaces
Alday & Maldacena conjectured an equivalence between string amplitudes in AdS5 ×S5 and null polygonal Wilson loops in planar N = 4 superYangMills (SYM). At strong coupling this identifies SYM amplitudes with (regularized) areas of minimal surfaces in AdS. In collaboration with Gaiotto, Sever & Vieira they introduced a Ysystem and a thermodynamic Bethe ansatze (TBA) expressing the complete integrability that could in principle be used to solve for the amplitude. These lectures will review the parts of this material that we need and use them to identify new geometric structures on the spaces of kinematics for super YangMills amplitudes. In AdS3, we find that the nontrivial part of these amplitudes at strong coupling, the remainder function, is the (pseudo)Kahler scalar for a (pseudo)hyperKaher geometry. It satisfies an integrable system and we give its Lax form. The result follows from a new perspective on Ysystems more generally as defining a natural twistor space associated to some integrable geometry. This connection to pseudohyperkahler and related geometries therefore extends to formfactors and full kinematics and suggests new structures underpinning the N=4 SYM amplitudes that might well be important beyond strong coupling.
Wednesday 1/17/24 – 1:30PM – Seminar Room 313
Speaker: Congkao Wen
Title: Exact integrated correlators in N=4 superYangMills theory
Over the past few years, it has been shown that, when integrating out the spacetime dependence with certain integration measures, some fourpoint correlation functions in N=4 superYangMills theory (N=4 SYM) can be computed exactly. These physical quantities are called integrated correlators. In perturbation, they are related to periods of certain conformal invariant Feynman integrals. Nonperturbatively, they are functions of (complexified) YangMills coupling, and transform under the Sduality of N=4 SYM. In this talk, I will review some of the recent developments regarding these integrated correlators.
WEEK 3: January 22 January 24, 2024
Monday 1/22/24: 10:30AM11:30AM – Seminar Room 313
Tuesday 1/23/24: 10:30AM11:30AM – Seminar Room – 313
Wednesday 1/24/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Mark Spradlin
Title: Cluster Algebras and Symbol Alphabets
Abstract: Modern perturbative calculations of multiloop amplitudes in planar N=4 SYM theory rely heavily on knowledge or assumptions about the types of functions that can appear and their singularity structure. I will review what is known, conjectured, and proposed about the connections between this structure and Grassmannian cluster algebras.
Thursday 1/25/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Song He
Title: The unity of colored scalars, pions and gluons
Abstract: I will report on a new discovery that allloop “stringy” amplitudes of tr phi^3 (the simplest theory of colored scalars) secretly contain the scattering amplitudes for pions and nonsupersymmetric gluons in arbitrary dimensions. In particular, tree amplitudes of tr phi^3 , nonlinear sigma model and YangMills theory are given by expanding around different kinematic points of the same function, the VenezianoKobaNielsen string amplitude, which in turn explains another surprise: tree amplitudes of all these colored theories have a hidden pattern of zeros and new factorizations near such zeros.
Friday 1/26/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Carolina Figueiredo
Title: Gluons from Surfaces
Abstract: Scattering amplitudes for the simplest theory of colored scalars— Tr \phi^3 theory — have been understood as arising from a counting problem associated with curves on a surface (arXiv:2309.15913). This formulation produces “stringy” integrals for the amplitudes, built off of variables defined on the surface, from which the field theory limit as α′→ 0 can easily be extracted. Recently, extensions of this approach to theories closer to the real world — in particular the nonlinear sigma model and YangMills theory — have been proposed (arXiv:2401.05483,arXiv:2401.00041). In this talk, we will focus on the gluon case.
WEEK 4: January 29 – February 2, 2024
Tuesday 1/30/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Aidan Herderschee
Title: Three Point Amplitudes in Matrix Theory
Abstract: The BFSS matrix model, a 1d matrix model that realizes 32 supercharges, is conjecturally dual to Mtheory in eleven dimensional asymptotically flat space and provides a concrete example of celestial holography. Although the model could be viewed as a simpler version of N=4 SYM, it is in many ways more poorly understood. For example, there is no systematic proof that BFSS amplitudes obey the eleven dimensional Lorentz symmetry of the bulk theory. I will give a short overview of 2312.12592 where the three point amplitude in BFSS is computed by relating it to an index computation. I will first give a quick introduction to BFSS and motivate the computation. I will then outline how to compute the index in the matrix model and its relation to the 3point amplitude. I will conclude with a short discussion of how one could use this result, in combination with other assumptions, to argue that generic BFSS npoint amplitudes are Lorentz symmetric in the largeN limit.
Wednesday 1/31/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Henrik Johansson
Title: Constructing NonPlanar Integrands for N=4 SYM
Abstract: The many successes of the planar sector of N=4 SYM have not yet spilled over to the corresponding nonplanar amplitudes, where the stateoftheart calculations are at modest 4pt or 5pt level. While the planar integrand has been bypassed in favor of powerful amplitudes bootstrap methods, the integrand is still needed for nonplanar N=4 SYM. The notion of a nonplanar integrand is sometimes contentious, but for practical purposes a welldefined integrand can be obtained through standard unitaritybased calculations. I will discuss two new methods for bootstrapping the nonplanar integrand of N=4 SYM, one of which was used to uniquely obtain a 6loop 4pt integrand without any input from cuts constructed from complicated state sums. The two methods are universal, in the sense that they apply to any massless gauge theory.
Thursday 2/1/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Andrew McLeod
Title: Bootstrapping Feynman Integrals via Landau Analysis
Abstract: Feynman integrals play a central role in perturbative quantum field theory calculations, and exhibit many intricate types of mathematical structure. In this talk, I will highlight recent progress that has been made towards untangling one important facet of this structure—the location and nature of their singularities. In particular, I will show how strong constraints can be placed on the analytic structure of Feynman integrals by connecting methods first pioneered by Landau to our modern understanding of the types of special functions that appear in perturbative computations. I will illustrate the power of these constraints by using them to bootstrap the complete functional form of several examples of Feynman integrals that involve both massive and massless particles.
Friday 2/2/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Kai Yan
Title: Novel Aspects of Energy Correlators
Abstract: Energy Correlator observables probe the distributions of energy flow in the final states of particle scattering experiments.They provide valuable data for studies ranging from conformal field theories to jet substructure, and a potential playground for novel onshell methods in scattering amplitudes. We propose the study of Npoint energy correlators in N=4 super YangMills theory, as an integrated N+1point super form factor of protected operators with manifest dual conformal symmetry. In the collinear limit, they admit parametric representations similar to Feynman loop integrals, linking to novel computational methods that operate directly in Feynman parametric space. We present the analytic result for the fourpoint energy correlator and comment on its singularity structures, which provide experiences for bootstrapping crosssection level observables.
WEEK 5: February 5 – February 9, 2024
Monday 2/5/24: 10:30AM11:30AM – Seminar Room 313
Tuesday 2/6/24: 10:30AM11:30AM – Seminar Room – 313
Wednesday 2/7/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Amit Sever
Title: The OPE approach for scattering amplitudes
Abstract: One approach for computing planar scattering amplitudes in N=4 SYM theory is based on an analogue of an operator product expansion (OPE) for these observables. In this minicourse, we will review the main ideas of the amplitude OPE. We will start at weak coupling, bootstrap the finitecoupling OPE building blocks, and end with a reconstruction of the strongcoupling minimal area. A summary of extensions of the amplitude OPE and related open questions will be given.
Thursday 2/8/24: 10:30AM11:30AM – Seminar Room 313
Speaker: Tianji Cai
Title: Transformers to transform Scattering Amplitudes Calculation
Abstract: AI for fundamental physics is now a burgeoning field, with numerous efforts pushing the boundaries of experimental and theoretical physics. In this talk, I will introduce a recent innovative application of Natural Language Processing to stateoftheart calculations for scattering amplitudes. Specifically, we use Transformers to predict the symbols at high loop orders of the threegluon form factors in planar N=4 Super YangMills theory. Our first results have demonstrated great promises of Transformers for amplitude calculations, opening the door for an exciting new scientific paradigm where discoveries and human insights are inspired and aided by AI.
Friday 2/9/24: 10:30AM11:30AM – Seminar Room 313
Speaker: Enrico Olivucci
Title: Multipoint Feynman Diagrams via Integrability
Abstract: Multipoint Feynman Diagrams (FD) in a ddimensional CFT are highly nontrivial functions of conformalinvariants. To understand the class of functions that describes conformal FD is an intriguing open problem for the perturbative description of CFTs in d=4 dimensions, and data are usually hard to access beyond few loops. Following A. Zamolodchikov I will argue that here exists a wide class of conformal FD where the problem can be treated due to the braid “startriangle” symmetry of the FD, allowing to formulate such integrals as partition functions of an Integrable spinmagnet in some infinitedimensional representation of the conformal group SO(1,d+1). In particular, I will concentrate on the class of planar 4d Fishnet multipoint integrals with disk topology and derive an integrabilitybased representation over the spectrum of separated variables. In the simplest case of multipoint generalization of DavydichevUsyukina Ladder integrals, I will explain how to get efficiently the lightconeOPE in multiple channels, at any loop order.
WEEK 6: February 12 – February 16, 2024
Monday 2/12/24: 10:30AM11:30AM – Seminar Room 313
Thursday 2/15/24: 1:30PM2:30PM Seminar Room – 313
Friday 2/16/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Lance Dixon
Title: Amplitude Bootstrap
Abstract: Planar N=4 SYM amplitudes (and form factors) are dual to lightlike polygonal Wilson loops (in a periodic space). They are nontrivial only for six or more gluons (three or more gluons). The spaces of functions which describe them are so restrictive that only a few constraints from the Pentagon OPE or other limits are needed to “write down the answer”, through seven loops in the sixgluon case, four loops in the sevengluon case, and eight loops for the threegluon form factor of the chiral part of the stressenergy tensor. I will review the construction of the relevant spaces of functions using the symbol and coaction. I will also describe a mysterious “antipodal selfduality”, which maps the fourgluon form factor into itself while reversing the order of all terms in its symbol, and which “explains” an antipodal duality between the threegluon form factor and the sixgluon amplitude.
Friday 2/16/24: 1:30PM – 2:30PM – Seminar Room – 313
Speaker: Zhenjie Li (SLAC)
Title: Kinematics, cluster algebras and Feynman integrals
Abstract:Cluster algebras are found in not only amplitudes but also Feynman integrals in recent years. In this talk, I will provide evidence how cluster algebras appear in the alphabet of some planar kinematics of conformal Feynman integrals in four dimensions. They can be identified as nontrivial subalgebras of the topdimensional Grassmannian G(4,n) corresponding to npoint massless kinematics. By sending a point to infinity, this method applies for nonconformal planar Feynman integrals. With dimension reduction, it also provides some insight into the cluster algebra of Feynman integrals in 3D theory.
WEEK 7: February 19 – February 23, 2024
Tuesday 2/20/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Chi Zhang
Title: Elliptic bootstrap program through Schubert analysis
Abstract: In this talk, I will briefly review the symbology for multiple polylogarithms and elliptic multiple polylogarithms with the sunrise integrals and the 10point doublebox integrals as examples. Then I will introduce the socalled Schubert problem and describe how to predict the symbol alphabet for the 12point doublebox integral using the Schubert problem and comment on the result obtained by the bootstrap program.
Wednesday 2/21/24: 10:30AM11:30AM – Seminar Room – 313
Thursday 2/22/24: 10:30AM11:30AM Seminar Room – 313
Friday 2/23/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: James Drummond
Title: Solving N=4 Super YangMills theory via Wilson Loops
Abstract: Scattering amplitudes are related to lightlike (super) Wilson loops in N=4 Super YangMills theory in the large N_c limit. I will recall some of the methods for computing such amplitudes/Wilson loops (e.g. BCFW recursion, Twistorial super Wilson loops and Qbar equations) and show that these methods extend to correlation functions of multiple Wilson loops.
WEEK 8: February 26 – March 1, 2024
Workshop: Mathematical Aspects of N=4 SuperYangMills Theory
WEEK 9: March 4 – March 8, 2024
Monday 3/4/24: 10:30AM11:30AM – Seminar Room 313
Tuesday 3/5/24: 10:30AM11:30AM – Seminar Room – 313
Wednesday 3/6/24: 10:30AM11:30AM – Seminar Room – 313
Speaker: Fernando Alday
Title: Tree level string amplitudes on AdS
Abstract: After reviewing properties of string theory amplitudes in flat space, in these lectures we will introduce a set of tools to construct treelevel string theory amplitudes on AdS Backgrounds, in a large radius expansion. This will combine the AdS/CFT duality, CFT tools, results from integrability and recent developments in number theory.
Organized by: D. Bernard, B. Bertini, F. H. L. Essler, V. Khemani and T. Prosen
Experimental advances in ultracold atomic physics and building quantum simulators have opened up new research areas in quantum manybody physics focused on inherently dynamical properties. Examples of fundamental questions that have been investigated in the last few years included characterizing quantum manybody chaos, describing the spreading of quantum information, defining and classifying novel “dynamical phases” in periodically driven and/or open systems and understanding the effects of quantum noise. Investigating these questions is intrinsically difficult as they pertain to nonequilibrium properties of interacting manyparticle quantum systems. Remarkable progress had been achieved by considering simplified models for quantum dynamics, socalled quantum circuits (QC). These retain the key property of spatial locality, but consider discrete time evolution based on sequences of simple quantum gates. These setups can be equivalently thought of as continuous in time but subject to a periodic driving.
QC allow the analysis of both unitary and nonunitary discrete time evolution, which describes noisy or monitored systems. The latter is of particular interest in relation to the technologicallydriven recent emergence of noisy, intermediatescale quantum devices
(NISQ). These exhibit environmental noise and decoherence and also allow partial quantum measurements during the dynamics (a key capability for error correction in future “faulttolerant” quantum computers). QC are particular classes of tensor networks, which have revolutionized our understanding of the role of quantum entanglement in manyparticle quantum systems and are the numerical method of choice for investigating quantum dynamics in low dimensions. One objective of studying quantum circuits has been to understand how to modify existing tensor network methods in order to overcome the socalled entanglement barrier in nonequilibrium dynamics.
A separate but closely related line of research has focused on formulating and solving paradigmatic models for stochastic continuoustime dynamics in extended systems. Here a key objective is to develop a quantum analogue of the celebrated macroscopic fluctuation
theory, which provides an effective description of transport and fluctuations in classical stochastic systems. A key stepping stone in this classical context was the formulation of exactly solvable models such as simple exclusion processes. Very recently quantum
versions of these processes have been formulated and it was shown that the noiseaveraged dynamics is described by Lindblad equations that can be mapped to unusual kinds of quantum integrable models. Interestingly, in particular limits and settings these models reduce to the extensively studied classical exclusion processes.
Our aim is to bring together scientists who have been at the forefronts of recent developments in quantum circuits, stochastic quantum dynamics, tensor networks and solvable classical stochastic processes and provide a platform for crossfertilization between these
currently only loosely connected communities. The Program will focus on two closely connected thematic centers of gravity : (i) exact results on open, stochastic, outofequilibrium systems and (ii) exact results on quantum circuits, chaotic or integrable.
This program will also be hosting a workshop: Fluctuations, Entanglements, and Chaos: Exact Results: August 28, 2023 September 1, 2023
Schedule of Program Talks:
DATE and TIME  TITLE  SPEAKER  ABSTRACT 

Tuesday 9/5 at 10:30am  Rise and fall of critical correlations after measurements 
Sara Murciano

Abstract 
Wednesday 9/6 at 10:30am  Hierarchical generalization of dual unitarity 
Pavel Kos

Abstract 
Thursday 9/7 at 10:30am  Temporal Entanglement in Chaotic Quantum Circuits 
Bruno Bertini

Abstract 
Friday 9/8 at 10:30am  Nonequilibrium O(N) models: Critical exceptional points, Goldstone limit cycles, and new nonequilibrium universality  Sebastian Diehl  Abstract 
Monday 9/11 at 10:30am  Converting entanglement into mixture: a new algorithm for longtime dynamics with tensor networks  Mari Carmen Bañuls  Abstract 
Tuesday 9/12 at 10:30am  Quantum jamming brings quantum mechanics to macroscopic scales  Maurizio Fagotti  Abstract 
Wednesday 9/13 at 10:30am  Symmetry Classification of Lindbladians and PTsymmetric Hamiltonians  Lucas Sa  Abstract 
Thursday 9/14 at 10:30am  TBA  Cheryne Jonay  
Friday 9/15 at 10:30am  Statistics of matrix elements in integrable models  Fabian Essler  Abstract 
Monday 9/18 at 10:30am  Operator dynamics in Floquet manybody systems  T. Yoshimura  Abstract 
Wednesday 9/20 at 10:30am  Can the macroscopic fluctuation theory be quantized? An introduction to QSSEP  L. Hruza  Abstract 
Thursday 9/21 at 10:30am  Chaos and Relaxation in a Dissipative SachdevYeKitaev Model  Jacobus J. Verbaarschot  Abstract 
Friday 9/22 at 10:30am  Playing with free probability in noisy manybody systems  Denis Bernard  Abstract 
Monday 9/25 at 10:30am  Spacetime dual cat and clock models  Austen Lamacraft  Abstract 
Tuesday 9/26 at 10:30am  Statistical mechanics insights into the complexity of tensor networks contractions  Romain Vasseur  Abstract 
Wednesday 9/27 at 10:30am  Floquet spin chains: Strong Modes, Almost Strong Modes, and Topological Defects  Aditi Mitra  Abstract 
Thursday 9/28 at 10:30am  Counting statistics of fermions (interacting and noninteracting) and the Gaussian free field  Pierre Le Doussal  Abstract 
Friday 9/29 at 10:30am  Integrable Digital Quantum Simulation: Generalized Gibbs Ensembles and Trotter Transitions  Lorenzo Piroli  Abstract 
Monday 10/2 at 10:30am  Correlation functions in GGEs: from the XX chain to the sineGordon model  Benjamin Doyon  Abstract 
Tuesday 10/3 at 10:30am  Nonlinear sigma model description of monitored free Majorana fermions  Michele Fava  Abstract 
Wednesday 10/4 at 10:30am  Entanglement Hamiltonians in quantum manybody systems  Viktor Eisler  Abstract 
Thursday 10/5 at 10:30am  Eigenoperator thermalization theory  Berislav Buca  Abstract 
]]>
DATE  TITLE  SPEAKER  ABSTRACT 

2/7/24  On Fermi surfaces: emergent symmetries and anomalies  Dominic Else  Abstract 
2/14/24  Equivariant localization for AdS/CFT  Pietro Benetti Genolini  Abstract 
2/28/24  Two dimensional QCD as a string theory  Ofer Aharony  Abstract 
3/6/24  Indranil Halder  
3/20/24  Yegor Zenkevich  
3/27/24  Nathan Haouzi  
4/3/24  Surya Raghavendran  
4/10/24  
4/17/24  Oscar Varela  
4/24/24   
5/1/24  
5/8/24  
5/15/24  Tarun Grover  
5/22/24  
5/29/24  Zohar Nussinov  
]]>
Talk Schedule:
Time  Title  Speaker  Location 
Monday October 31  
10:30am  Hyperuniformity and its connection to number theory and discrete geometry  Salvatore Torquato  SCGP 313 
Monday October 31  
1:30pm  Numbers from quantum field theory (lectures III and IV)  Karen Yeats  SCGP 313 
Tuesday November 1  
10:30am 
The many faces of number theory in string theory

Abhiram Kidambi  SCGP 313 
Wednesday November 2  
10:30am  Numbers from quantum field theory (lectures III and IV)  Karen Yeats  SCGP 313 
Monday November 7  
10:30am 
KatzSarnak families and the Riemann hamiltonian

Mark Srednicki

SCGP 313 
Tuesday November 8  
10:30am 
H = xp, the Landau model and the Dirac equation

German Sierra  SCGP 313 
Wednesday November 9  
10:30am  Modular forms and their Lfunctions  David LowryDuda  SCGP 313 
Thursday November 10  
10:30am  The Lerch zeta function and the Heisenberg group  Jeff Lagarias  SCGP 313 
Friday November 11  
10:30am  Moments of the Hurwitz zeta function  Anurag Sahay  SCGP 313 
Tuesday November 15  
10:30am  Uniform distribution and geometric incidence theory  Ayla Gafni  SCGP 313 
Thursday, November 17  
10:30am  TBA  Israel Klitch  SCGP 313 
Friday, November 18  
10:30am  When do symplectic Lfunctions have square roots?  Amina Abdurrahman  SCGP 313 
The interplay between Number Theory and Physics has a long tradition, as illustrated by several examples and many initiatives of the past. A wellknow example is the tantalizing connection between Random Matrix Theory and the statistical properties of the zeros of the Riemann zeta function and other Lfunctions. This connection opened the avenue to the application of techniques that first appeared in Nuclear Physics to Number Theory. Random Matrix Theory has proved to be a golden mine of profound ideas which span from the description of random media to cold atom fermions in magnetic trap. It is worth to mention that it is along this direction the attempt to address the Riemann Hypothesis employing concepts from Quantum Mechanics or Statistical Physics. String theory has also provided a playground for the connections with number theory and algebraic geometry, playing an important role in the discovery of mirror symmetry. Many novel ideas are now emerging relating string theory and the geometry of CalabiYau manifolds to Mock modular forms and paramodular forms. Finally, Number Theory has also played a crucial role in Quantum Information starting from the Shor’s algorithm that reduces the exponential cost of factorizing integers in a classical computer to a polynomial cost using a quantum computer. The recent construction of small quantum computers suggests that quantum algorithms based on Number Theory will play a fundamental role in the near future with a huge impact in basic sciences and technology.
There is also a workshop associated with this event: Number Theory And Physics.
]]>Organized by: Sergio Cacciatori (Università degli studi dell’Insubria), Samuel Grushevsky (SCGP), Alexander Polishchuk (University of Oregon)
A supermanifold is the generalization of a usual manifold when some of the coordinates are even variables, and some are odd. The mathematical foundations of supergeometry were established in the 1970s and 1980s. While much of the motivation for this came from supersymmetric theories in physics, the mathematical study became possible largely due to the development of the language of algebraic and complex geometry in the preceding decades. For the following 30 years or so, the progress of supergeometry was somewhat modest, although there were some substantial developments in other mathematical aspects of supersymmetry (eg. Lie superalgebras). Recently, the interest in supergeometry has revived, from physicists reexamining the foundations of superstring scattering, from the physical interest in mirror symmetry for supermanifols, and from mathematicians finally nearing a rigorous construction and study of the moduli of supercurves, and exploring related foundational questions in algebraic supergeometry. The program will bring together mathematicians and physicists who have been recently working on supergeometry, aiming to create a cohesive community of researchers and to let the physical intuition and mathematical rigour benefit from each other. There is also a workshop associated with this event: SuperGeometry and SuperModuli: March 2731, 2023
Schedule of Program Talks:
*All talks will be held in room 313 unless otherwise noted
DATE and TIME  TITLE  SPEAKER  ABSTRACT 

Mon 4/3 at 10:30am  Minicourse on moduli of SUSY curves I  Alexander Polishchuk  
Tues 4/4 at 1:30pm  Universal de Rham/Spencer double complex on a supermanifold  Sergio Cacciatori  
Wed 4/5 at 10:30am  Minicourse on moduli of SUSY curves II  Alexander Polishchuk  
Thurs 4/6 at 1:30pm  Towards super Teichmuller spin Osp(12) TQFT  Nezhla Aghaei  Abstract 
Fri 4/7 at 10:30am  Minicourse on moduli of SUSY curves III  Alexander Polishchuk  
Tues 4/11 at 10:30am  Supergravity and supergeometry I  Pietro Antonio Grassi  
Wed 4/12 at 10:30am  Supergravity and supergeometry II  Pietro Antonio Grassi  
Thurs 4/13 at 1:30pm  SUSY operads  Enno Kessler  
Fri 4/14 at 1:30pm  Compactification of moduli of SUSY curves  Yehao Zhou  
Mon 4/17 at 10:30am  CS forms: a consistent formalism for integrals on complex supermanifolds  Dmitry Vaintrob  
Wed 4/19 at 10:30am  Compactification of moduli of SUSY curves – details of the construction  Yehao Zhou  
Mon 4/24 at 10:30am  The supermoduli space M_{0,0,n}  Alexander Voronov  
Wed 4/26 at 10:30am  Volumes of moduli spaces of super hyperbolic surfaces with Ramond punctures.  Paul Norbury  
Mon 5/1 at 10:30am  Microformal morphisms of supermanifolds and homotopy algebras  Theodore Voronov  
Tues 5/2 at 10:30am  Log geometry and Log orbifold compactification of the space of superconformal curves  Dmitry Vaintrob  
Wed 5/3 at 10:30am  Classical Cohomological Field Theory  Shuhan Jiang  
Wed 5/3 at 1:30pm in room 102  Microformal morphisms of supermanifolds and homotopy algebras, part II  Theodore Voronov  
Thurs 5/4 at 10:30am  Super Pluecker map – towards super cluster algebras  Ekaterina Shemyakova 