Strategyproof-Exposing Mechanisms Descriptions
2022-09-14 12:00 - 13:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Yannai Gonczarowski (Harvard)

Title: Strategyproof-Exposing Mechanisms Descriptions
Abstract: One of the crowning achievements of the field of Mechanism Design has been the design and usage of the so-called “Deferred Acceptance” matching algorithm. Designed in 1962 and awarded the Nobel Prize in 2012, this algorithm has been used around the world in settings ranging from matching students to schools to matching medical doctors to residencies. A hallmark of this algorithm is that unlike many other matching algorithms, it is “strategy-proof”: participants can never gain by misreporting their preferences (say, over schools) to the algorithm. Alas, this property is far from apparent from the algorithm description. Its mathematical proof is so delicate and complex, that (for example) school districts in which it is implemented do not even attempt to explain to students and parents why this property holds, but rather resort to an appeal to authority: Nobel laureates have proven this property, so one should listen to them. Unsurprisingly perhaps, there is a growing body of evidence that participants in Deferred Acceptance attempt (unsuccessfully) to “game it,” which results in a suboptimal match for themselves and for others.
By developing a novel framework of algorithm description simplicity—grounded at the intersection between Economics and Computer Science—we present a novel, starkly different, yet equivalent, description for the Deferred Acceptance algorithm, which, in a precise sense, makes its strategyproofness far more apparent. Our description does have a downside, though: some other of its most fundamental properties—for instance, that no school exceeds its capacity—are far less apparent than from all traditional descriptions of the algorithm. Using the theoretical framework that we develop, we mathematically address the question of whether and to what extent this downside is unavoidable, providing a possible explanation for why our description of the algorithm has eluded discovery for over half a century. Indeed, it seems that in the design of all traditional descriptions of the algorithm, it was taken for granted that properties such as no capacity getting exceeded should be apparent. Our description emphasizes the property that is important for participants to correctly interact with the algorithm, at the expense of properties that are mostly of interest to policy makers, and thus has the potential of vastly improving access to opportunity for many populations. Our theory provides a principled way of recasting algorithm descriptions in a way that makes certain properties of interest easier to explain and grasp, which we also support with behavioral experiments in the lab.
Joint work with Ori Heffetz and Clayton Thomas.

Breaking the one-mind-barrier in mathematics using formal verification
2022-09-14 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Johan Commelin, Mathematisches Institut, Albert-Ludwigs-Universität Freiburg
Title: Breaking the one-mind-barrier in mathematics using formal verification
Abstract: In this talk I will argue that formal verification helps break the one-mind-barrier in mathematics. Indeed, formal verification allows a team of mathematicians to collaborate on a project, without one person understanding all parts of the project. At the same time, it also allows a mathematician to rapidly free mental RAM in order to work on a different component of a project. It thus also expands the one-mind-barrier.
I will use the Liquid Tensor Experiment as an example, to illustrate the above two points. This project recently finished the formalization of the main theorem of liquid vector spaces, following up on a challenge by Peter Scholze.
Video

The Gregory-Laflamme instability of black strings revisited
2022-09-15 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar

Title: The Gregory-Laflamme instability of black strings revisited

Abstract: In this talk I will discuss our recent work that reproduces and extends the famous work of Lehner and Pretorius on the end point of the Gregory-Laflamme instability of black strings. We consider black strings of different thicknesses and our numerics allow us to get closer to the singularity than ever before. In particular, while our results support the picture of the formation of a naked singularity in finite asymptotic time, the process is more complex than previously thought. In addition, we obtain some hints about the nature of the singularity that controls the pinch off of the string.

Derivation of AdS/CFT for Vector Models
2022-09-16 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar

Speaker: Shai Chester

Title: Derivation of AdS/CFT for Vector Models
Abstract: We derive an explicit map at finite N between the singlet sector of the free and critical O(N) and U(N) vector models in any spacetime dimension above two, and a bulk higher spin theory in anti-de Sitter space in one higher dimension. For the boundary theory, we use the bilocal formalism of Jevicki et al to restrict to the singlet sector of the vector model. The bulk theory is defined from the boundary theory via our mapping, and is a consistent quantum higher spin theory with a well defined action. Our mapping relates bilocal operators in the boundary theory to higher spin fields in the bulk, while single trace local operators in the boundary theory are related to boundary values of higher spin fields. We also discuss generalizations of the map to gauge theories, and at finite temperature.

The story of the information paradox
2022-09-19 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar

Speaker: Samir Mathur (Ohio State)

Title: The story of the information paradox

Abstract: In 1975 Hawking argued that black hole evaporation would lead to a loss of unitarity in quantum theory. The small corrections theorem made Hawking’s argument into a precise statement: if semiclassical physics hold to leading order in any gently curved region of spacetime, then there can be no resolution to the paradox. In string theory, whenever people have been able to construct microstates explicutly, the states turned out to be horizon sized objects (fuzzballs) with no horizon; such a structure of microstates resolves the information paradox since their is no pair creation at a vacuum horizon. There have been a set of parallel attempts to resolve the paradox (with ideas involving wormholes, islands etc) where the horizon is smooth in some leading approximation. An analysis of such models however indicated that in each case the exact quantum gravity theory would either have to be nonunitary or to have dynamics at infinity that is conflict with usual low energy physics in the lab.

Geometric test for topological states of matter
2022-09-21 09:00 - 10:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Semyon Klevtsov, University of Strasbourg
Title: Geometric test for topological states of matter
Abstract: We generalize the flux insertion argument due to Laughlin, Niu-Thouless-Tao-Wu, and Avron-Seiler-Zograf to the case of fractional quantum Hall states on a higher-genus surface. We propose this setting as a test to characterise the robustness, or topologicity, of the quantum state of matter and apply our test to the Laughlin states. Laughlin states form a vector bundle, the Laughlin bundle, over the Jacobian – the space of Aharonov-Bohm fluxes through the holes of the surface. The rank of the Laughlin bundle is the
degeneracy of Laughlin states or, in presence of quasiholes, the dimension of the corresponding full many-body Hilbert space; its slope, which is the first Chern class divided by the rank, is the Hall conductance. We compute the rank and all the Chern classes of Laughlin bundles for any genus and any number of quasiholes, settling, in particular, the Wen-Niu conjecture. Then we show that Laughlin bundles with non-localized quasiholes are not projectively flat and that the Hall current is precisely quantized only for the states with localized quasiholes. Hence our test distinguishes these states from the full many-body Hilbert space. Based on joint work with Dimitri Zvonkine (CNRS, University of Paris-Versaille).

Limit and potential of adaptive immunity
2022-09-21 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar

Speaker: Shenshen Wang, UCLA

Title: Limit and potential of adaptive immunity

Abstract: The adaptive immune system is able to learn from past experiences to better fit an
unforeseen future. This is made possible by a diverse and dynamic repertoire of cells
expressing unique antigen receptors and capable of rapid Darwinian evolution within an
individual. However, naturally occurring immune responses exhibit limits in efficacy,
speed and capacity to adapt to novel challenges. In this talk, I will discuss theoretical
frameworks we developed to (1) explore functional impacts of non-equilibrium antigen
recognition, and (2) identify conditions under which natural selection acting local in time
can find adaptable solutions favorable in the long run, through exploiting environmental
variations and functional constraints.

Moduli spaces of graphs
2022-09-21 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium

Speaker: Melody Chan, Brown

Title: Moduli spaces of graphs

Abstract: A metric graph is a graph—a finite network of vertices and edges—together with a prescription of a positive real length on each edge. I’ll use the term “moduli space of graphs” to refer to certain combinatorial spaces—think simplicial complexes—that furnish parameter spaces for metric graphs. There are different flavors of spaces depending on some additional choices of decorations on the graphs, but roughly, each cell parametrizes all possible metrizations of a fixed combinatorial graph. Many flavors of these moduli spaces have been in circulation for a while, starting with the work of Culler-Vogtmann in the 1980s on Outer Space. They have also recently played an important role in some recent advances using tropical geometry to study the topology of moduli spaces of curves and other related spaces. These advances give me an excuse to give what I hope will be an accessible introduction to moduli spaces of graphs and their connections with geometry.

A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
2022-09-22 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar

Speaker: Nikolaos Athanasiou

Title: A scale-critical trapped surface formation criterion for the Einstein-Maxwell system

Abstract: Few notions within the realm of mathematical physics succeed in capturing the imagination and inspiring awe as well as that of a black hole. First encountered in the Schwarzschild solution, discovered a few months after the presentation of the Field Equations of General Relativity at the Prussian Academy of Sciences, the black hole as a mathematical phenomenon accompanies and prominently features within the history of General Relativity since its inception. In this talk we will lay out a brief history of the question of dynamical black hole formation in General Relativity and discuss a result, in collaboration with Xinliang An, on a scale-critical trapped surface formation criterion for the Einstein-Maxwell system.

CMSA/MATH Fall Gathering
2022-09-23 04:30 - 18:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
CMSA/MATH Fall Gathering
Friday, Sep 23, 2022
4:30–6:00 pm

All CMSA and Math affiliates are invited.

Random determinants, the elastic manifold, and landscape complexity beyond invariance
2022-09-23 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Ben McKenna
Title: Random determinants, the elastic manifold, and landscape complexity beyond invariance
Abstract: The Kac-Rice formula allows one to study the complexity of high-dimensional Gaussian random functions (meaning asymptotic counts of critical points) via the determinants of large random matrices. We present new results on determinant asymptotics for non-invariant random matrices, and use them to compute the (annealed) complexity for several types of landscapes. We focus especially on the elastic manifold, a classical disordered elastic system studied for example by Fisher (1986) in fixed dimension and by Mézard and Parisi (1992) in the high-dimensional limit. We confirm recent formulas of Fyodorov and Le Doussal (2020) on the model in the Mézard-Parisi setting, identifying the boundary between simple and glassy phases. Joint work with Gérard Ben Arous and Paul Bourgade.

Candidates for Non-Supersymmetric Dualities
2022-09-26 09:00 - 10:30 | Virtual
Quantum Matter in Mathematics and Physics
Speaker: Avner Karasik (University of Cambridge, UK)
Title: Candidates for Non-Supersymmetric Dualities
Abstract: In the talk I will discuss the possibility and the obstructions of finding non-supersymmetric dualities for 4d gauge theories. I will review consistency conditions based on Weingarten inequalities, anomalies and large N, and clarify some subtle points and misconceptions about them. Later I will go over some old and new examples of candidates for non-supersymmetric dualities. The will be based on 2208.07842

Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow
2022-09-28 09:00 - 10:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Ruihua Fan, Harvard University
Title: Extracting the quantum Hall conductance from a single bulk wavefunction from the modular flow

Abstract: One question in the study of topological phases is to identify the topological data from the ground state wavefunction without accessing the Hamiltonian. Since local measurement is not enough, entanglement becomes an indispensable tool. Here, we use modular Hamiltonian (entanglement Hamiltonian) and modular flow to rephrase previous studies on topological entanglement entropy and motivate a natural generalization, which we call the entanglement linear response. We will show how it embraces a previous work by Kim&Shi et al on the chiral central charge, and furthermore, inspires a new formula for the quantum Hall conductance.

References: https://arxiv.org/abs/2206.02823, https://arxiv.org/abs/2208.11710

The Tree Property and uncountable cardinals
2022-09-28 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Dima Sinapova (Rutgers University)
Title: The Tree Property and uncountable cardinals
Abstract: In the late 19th century Cantor discovered that there are different levels of infinity. More precisely he showed that there is no bijection between the natural numbers and the real numbers, meaning that the reals are uncountable. He then went on to discover a whole hierarchy of infinite cardinal numbers. It is natural to ask if finitary and countably infinite combinatorial objects have uncountable analogues. It turns out that the answer is yes.
We will focus on one such key combinatorial property, the tree property. A classical result from graph theory (König’s infinity lemma) shows the existence of this property for countable trees. We will discuss what happens in the case of uncountable trees.

Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
2022-09-28 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics
Speaker: Surya Ganguli, Stanford University

Title: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling

Abstract: Statistical mechanics and neural network theory have long enjoyed fruitful interactions. We will review some of our recent work in this area and then focus on two vignettes. First we will analyze the high dimensional geometry of neural network error landscapes that happen to arise as the classical limit of a dissipative many-body quantum optimizer. In particular, we will be able to use the Kac-Rice formula and the replica method to calculate the number, location, energy levels, and Hessian eigenspectra of all critical points of any index. Second we will review recent work on neural power laws, which reveal that the error of many neural networks falls off as a power law with network size or dataset size. Such power laws have motivated significant societal investments in large scale model training and data collection efforts. Inspired by statistical mechanics calculations, we show both in theory and in practice how we can beat neural power law scaling with respect to dataset size, sometimes achieving exponential scaling, by collecting small carefully curated datasets rather than large random ones.

References: Y. Bahri, J. Kadmon, J. Pennington, S. Schoenholz, J. Sohl-Dickstein, and S. Ganguli, Statistical mechanics of deep learning, Annual Reviews of Condensed Matter Physics, 2020.

Sorscher, Ben, Robert Geirhos, Shashank Shekhar, Surya Ganguli, and Ari S. Morcos. 2022. Beyond Neural Scaling Laws: Beating Power Law Scaling via Data Pruning https://arxiv.org/abs/2206.14486 (NeurIPS 2022).

General-relativistic viscous fluids
2022-09-29 10:30 - 11:30 | Virtual
General Relativity Seminar
Speaker: Marcelo Disconzi, Vanderbilt University
Title: General–relativistic viscous fluids

Abstract: The discovery of the quark-gluon plasma that forms in heavy-ion collision experiments provides a unique opportunity to study the properties of matter under extreme conditions, as the quark-gluon plasma is the hottest, smallest, and densest fluid known to humanity. Studying the quark-gluon plasma also provides a window into the earliest moments of the universe, since microseconds after the Big Bang the universe was filled with matter in the form of the quark-gluon plasma. For more than two decades, the community has intensely studied the quark-gluon plasma with the help of a rich interaction between experiments, theory, phenomenology, and numerical simulations. From these investigations, a coherent picture has emerged, indicating that the quark-gluon plasma behaves essentially like a relativistic liquid with viscosity. More recently, state-of-the-art numerical relativity simulations strongly suggested that viscous and dissipative effects can also have non-negligible effects on gravitational waves produced by binary neutron star mergers. But despite the importance of viscous effects for the study of such systems, a robust and comprehensive theory of relativistic fluids with viscosity is still lacking. This is due, in part, to difficulties to preserve causality upon the inclusion of viscous and dissipative effects into theories of relativistic fluids. In this talk, we will survey the history of the problem and report on a new approach to relativistic viscous fluids that addresses these issues.

GLSM, Homological projective duality and nc resolutions
2022-09-30 09:30 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Mauricio Romo, Tsinghua University
Title: GLSM, Homological projective duality and nc resolutions

Abstract: Kuznetsov’s Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.

Kahler geometry in twisted materials
2022-09-30 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Jie Wang
Title: Kahler geometry in twisted materials
Abstract: Flatbands are versatile platform for realizing exotic quantum phases due to the enhanced interactions. The canonical example is Landau level where fractional quantum Hall physics exists. Although interaction is strong, the fractional quantum Hall effect is relatively well understood thanks to its model wavefunction, exact parent Hamiltonian, conformal field theory analogous and other exact aspects. In generic flatbands, the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. It is commonly believed that the non-uniform geometries destroy these exact properties of fractional quantum Hall physics, making many-body states less stable in flatbands.
In this talk, I will disprove this common belief by showing a large family of flatbands (ideal flatbands) where quantum geometries can be highly non-uniform, but still exhibit exact properties such as model wavefunctions, density algebra, exact parent Hamiltonians. I will discuss both the theory of ideal flatband, its experimental realization in Dirac materials as well as implications.

Holomorphic Twists and Confinement in N=1 SYM
2022-10-04 09:30 - 11:00 | Virtual
Quantum Matter Seminar
Speaker: Justin Kulp (Perimeter Institute)
Title: Holomorphic Twists and Confinement in N=1 SYM
Abstract: Supersymmetric QFT’s are of long-standing interest for their high degree of solvability, phenomenological implications, and rich connections to mathematics. In my talk, I will describe how the holomorphic twist isolates the protected quantities which give SUSY QFTs their potency by restricting to the cohomology of one supercharge. I will briefly introduce infinite dimensional symmetry algebras, generalizing Virasoro and Kac-Moody symmetries, which emerge. Finally, I will explain a potential novel UV manifestation of confinement, dubbed “holomorphic confinement,” in the example of pure SU(N) super Yang-Mills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.

Minerva: Solving Quantitative Reasoning Problems with Language Models
2022-10-05 14:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Guy Gur-Ari, Google Research
Title: Minerva: Solving Quantitative Reasoning Problems with Language Models
Abstract: Quantitative reasoning tasks which can involve mathematics, science, and programming are often challenging for machine learning models in general and for language models in particular. We show that transformer-based language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, math-focused dataset. Performance can be further improved using prompting and sampling techniques including chain-of-thought and majority voting. Minerva, a model that combines these techniques, achieves SOTA on several math and science benchmarks. I will describe the model, its capabilities and limitations.

Quantum statistical mechanics of charged black holes and strange metals
2022-10-05 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Please note this colloquium will be held at a special time: 4:00-5:00 pm.
Speaker: Subir Sachdev (Harvard)
Title: Quantum statistical mechanics of charged black holes and strange metals

Abstract: The Sachdev-Ye-Kitaev model was introduced as a toy model of interacting fermions without any particle-like excitations. I will describe how this toy model yields the universal low energy quantum theory of generic charged black holes in asymptotically 3+1 dimensional Minkowski space. I will also discuss how extensions of the SYK model yield a realistic theory of the strange metal phase of correlated electron systems.

Slides: cmsa22

Duality in Einstein’s Gravity
2022-10-06 10:30 - 23:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Uri Kol, CMSA

Title: Duality in Einstein’s Gravity
Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
2022-10-07 09:30 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Sam Bardwell-Evans, Boston University

Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.

Principal flow, sub-manifold and boundary
2022-10-07 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Zhigang Yao
Title: Principal flow, sub-manifold and boundary
Abstract: While classical statistics has dealt with observations which are real numbers or elements of a real vector space, nowadays many statistical problems of high interest in the sciences deal with the analysis of data which consist of more complex objects, taking values in spaces which are naturally not (Euclidean) vector spaces but which still feature some geometric structure. I will discuss the problem of finding principal components to the multivariate datasets, that lie on an embedded nonlinear Riemannian manifold within the higher-dimensional space. The aim is to extend the geometric interpretation of PCA, while being able to capture the non-geodesic form of variation in the data. I will introduce the concept of a principal sub-manifold, a manifold passing through the center of the data, and at any point on the manifold extending in the direction of highest variation in the space spanned by the eigenvectors of the local tangent space PCA. We show the principal sub-manifold yields the usual principal components in Euclidean space. We illustrate how to find, use and interpret the principal sub-manifold, by which a principal boundary can be further defined for data sets on manifolds.

The Penrose Inequality as a Constraint on Low Energy Quantum Gravity
2022-10-11 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar

Speaker: Aasmund Folkestad (MIT)

Title: The Penrose Inequality as a Constraint on Low Energy Quantum Gravity

Abstract: In this talk, I argue that the Penrose inequality (PI) can be used to constrain low energy theories compatible AdS/CFT, and possibly also quantum gravity in flat space. Focusing on AdS/CFT, it is shown that the PI can be violated for minimally coupled scalar fields, and I produce exclusion plots on couplings that respect the PI. I also present numerical evidence that top-down scalar theories and supersymmetric theories respect the PI. Finally, similar to the Breitenlohner-Freedman bound, I give a necessary condition for the stability AdS that constrains coupling constants (beyond the scalar mass).

Engineering topological phases with a superlattice potential
2022-10-12 09:00 - 10:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Jennifer Cano (Stony Brook and Flatiron Institute)
Title: Engineering topological phases with a superlattice potential

Abstract: We propose an externally imposed superlattice potential as a platform for manipulating topological phases, which has both advantages and disadvantages compared to a moire superlattice. In the first example, we apply the superlattice potential to the 2D surface of a 3D topological insulator. The superlattice potential creates tunable van Hove singularities, which, when combined with strong spin-orbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long sought-after goal of realizing spontaneous magnetic order on the surface of a 3D TI. In the second example, we show that a superlattice potential applied to Bernal-stacked bilayer graphene can generate flat Chern bands, similar to in twisted bilayer graphene, whose bandwidth can be as small as a few meV. The superlattice potential offers flexibility in both lattice size and geometry, making it a promising alternative to achieve designer flat bands without a moire heterostructure.

Complete disorder is impossible: Some topics in Ramsey theory
2022-10-12 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: James Cummings,Carnegie Mellon University
Title: Complete disorder is impossible: Some topics in Ramsey theory
Abstract: The classical infinite Ramsey theorem states that if we colour pairs of natural numbers using two colours, there is an infinite set all of whose pairs get the same colour. This is the beginning of a rich theory, which touches on many areas of mathematics including graph theory, set theory and dynamics. I will give an overview of Ramsey theory, emphasizing the diverse ideas which are at play in this area.

Strong Cosmic Censorship
2022-10-13 10:30 - 23:30 | Virtual
General Relativity Seminar

Speaker: Professor Oscar Dias (University of Southampton)

Title: Strong Cosmic Censorship
Abstract: Generically, strong cosmic censorship (SCC) is the statement that physics within general relativity should be predicted from initial data prescribed on a Cauchy hypersurface. In this talk I will review how fine-tuned versions of SCC have been formulated and evolved along the last decades up to the point where we believe that Christodoulou’s version is true in asymptotically flat spacetimes. However, I will also describe that in recent years it was found that this is no longer necessarily true for some other backgrounds, namely in some de Sitter (with a positive cosmological constant) spacetimes or even in rotating BTZ black holes in 3-dimensional Anti-de Sitter spacetime. Finally, I will discuss some possibilities (quantum effects, non-smooth initial data,…) that might restore SCC in those backgrounds where the standard formulation of the conjecture is violated.

Singularities of the quantum connection on a Fano variety
2022-10-14 09:30 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar

Speaker: Daniel Pomerleano, UMass Boston
Title: Singularities of the quantum connection on a Fano variety
Abstract: The small quantum connection on a Fano variety is one of the simplest objects in enumerative geometry. Nevertheless, it is the subject of far-reaching conjectures known as the Dubrovin/Gamma conjectures. Traditionally, these conjectures are made for manifolds with semi-simple quantum cohomology or more generally for Fano manifolds whose quantum connection is of unramified exponential type at q=infty.
I will explain a program, joint with Paul Seidel, to show that this unramified exponential type property holds for all Fano manifolds M carrying a smooth anticanonical divisor D. The basic idea of our argument is to view these structures through the lens of a noncommutative Landau-Ginzburg model intrinsically attached to (M, D).

Quantum magnet chains and Kashiwara crystals
2022-10-14 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Leonid Rybnikov, Harvard CMSA/National Research University Higher School of Economics
Title: Quantum magnet chains and Kashiwara crystals
Abstract: Solutions of the algebraic Bethe ansatz for quantum magnet chains are, generally, multivalued functions of the parameters of the integrable system. I will explain how to compute some monodromies of solutions of Bethe ansatz for the Gaudin magnet chain. Namely, the Bethe eigenvectors in the Gaudin model can be regarded as a covering of the Deligne-Mumford moduli space of stable rational curves, which is unramified over the real locus of the Deligne-Mumford space. The monodromy action of the fundamental group of this space (called cactus group) on the eigenlines can be described very explicitly in purely combinatorial terms of Kashiwara crystals — i.e. combinatorial objects modeling the tensor category of finite-dimensional representations of a semisimple Lie algebra g. More specifically, this monodromy action is naturally equivalent to the action of the same group by commutors (i.e. combinatorial analog of a braiding) on a tensor product of Kashiwara crystals. This is joint work with Iva Halacheva, Joel Kamnitzer, and Alex Weekes.
