### Representation Theory, Calabi–Yau Manifolds, and Mirror Symmetry

On November 28 – Dec 1, 2022, the CMSA will host a Workshop on Representation...

Read More
Opens in a new window
Opens an external site
Opens an external site in a new window

On November 28 – Dec 1, 2022, the CMSA will host a Workshop on Representation...

Read More(Dates TBA) In March 2023 Andrea Bertozzi (UCLA) will give two lectures hosted by the...

Read MoreCMSA/Tsinghua Math-Science Literature Lecture Prof. Hugh Woodin will present a lecture in the CMSA/Tsinghua Math-Science...

Read More«

»

Sun | Mon | Tue | Wed | Thu | Fri | Sat |
---|---|---|---|---|---|---|

September | September | September | September | September | September | 1 |

2 | 3 | 4 - Holomorphic Twists and Confinement in N=1 SYM
**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.
| 5 - Minerva: Solving Quantitative Reasoning Problems with Language ModelsCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**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 metalsCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**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.
| 6 - Duality in Einstein’s GravityCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**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.
| 7 - Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau SurfacesCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Algebraic Geometry in String Theory Seminar****Speake**r: 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 boundaryCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**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.
| 8 |

9 | 10 - Columbus Day (Federal) / Indigenous Peoples Day (City of Cambridge)
Holiday: Columbus Day (Federal) / Indigenous Peoples’ Day (City of Cambridge)
| 11 - The Penrose Inequality as a Constraint on Low Energy Quantum GravityCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**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).
| 12 - Engineering topological phases with a superlattice potentialCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**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 theoryCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Colloquium****Title:**Complete disorder is impossible: Some topics in Ramsey theory**Speaker:**James Cummings,**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.
| 13 | 14 - CMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Algebraic Geometry in String Theory Seminar**Speaker: Daniel Pomerleano, UMass Boston - Member Seminar: Title TBACMSA, 20 Garden Street, Cambridge, MA 02138 USA
Speaker: Leonid Rybnikov
| 15 |

16 | 17 | 18 | 19 - Colloquium: Title TBACMSA, 20 Garden Street, Cambridge, MA 02138 USA
Colloquium - Symmetric Mass GenerationCMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Topological Quantum Matter Seminar****Speaker:**Yizhuang You, UC San Diego**Title:**Symmetric Mass Generation**Abstract:**Symmetric mass generation (SMG) is a novel mechanism for massless fermions to acquire a mass via a strong-coupling non-perturbative interaction effect. In contrast to the conventional Higgs mechanism for fermion mass generation, the SMG mechanism does not condense any fermion bilinear coupling and preserves the full symmetry. It is connected to a broad range of topics, including anomaly cancellation, topological phase classification, and chiral fermion regularization. In this talk, I will introduce SMG through toy models, and review the current understanding of the SMG transition. I will also mention recent numerical efforts to investigate the SMG phenomenon. I will conclude the talk with remarks on future directions.
| 20 | 21 - CMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Algebraic Geometry in String Theory Seminar**Speaker:Nicolo Piazzalunga, Rutgers - Member Seminar: Title TBACMSA, 20 Garden Street, Cambridge, MA 02138 USA
Speaker: David Zuckerman
| 22 |

23 | 24 | 25 | 26 - Kähler bands—Chern insulators, holomorphicity and induced quantum geometryCMSA, 20 Garden Street, Cambridge, MA 02138 USATopological Quantum Matter Seminar
**Speaker:**Bruno Mera, Tohoku University**Title:**Kähler bands—Chern insulators, holomorphicity and induced quantum geometry**Abstract:**The notion of topological phases has dramatically changed our understanding of insulators. There is much to learn about a band insulator beyond the assertion that it has a gap separating the valence bands from the conduction bands. In the particular case of two dimensions, the occupied bands may have a nontrivial topological twist determining what is called a Chern insulator. This topological twist is not just a mathematical observation, it has observable consequences—the transverse Hall conductivity is quantized and proportional to the 1st Chern number of the vector bundle of occupied states over the Brillouin zone. Finer properties of band insulators refer not just to the topology, but also to their geometry. Of particular interest is the momentum-space quantum metric and the Berry curvature. The latter is the curvature of a connection on the vector bundle of occupied states. The study of the geometry of band insulators can also be used to probe whether the material may host stable fractional topological phases. In particular, for a Chern band to have an algebra of projected density operators which is isomorphic to the W∞ algebra found by Girvin, MacDonald and Platzman—*the GMP algebra*—in the context of the fractional quantum Hall effect, certain geometric constraints, associated with the*holomorphic*character of the Bloch wave functions, are naturally found and they enforce a compatibility relation between the quantum metric and the Berry curvature of the band. The Brillouin zone is then endowed with a*Kähler structure*which, in this case, is also translation-invariant (flat). Motivated by the above, we will provide an overview of the geometry of Chern insulators from the perspective of Kähler geometry, introducing the notion of a Kähler band which shares properties with the well-known ideal case of the lowest Landau level. Furthermore, we will provide a prescription, borrowing ideas from geometric quantization, to generate a flat Kähler band in some appropriate asymptotic limit. Such flat Kähler bands are potential candidates to host and realize fractional Chern insulating phases. Using geometric quantization arguments, we then provide a natural generalization of the theory to all even dimensions.References:[1] Tomoki Ozawa and Bruno Mera. Relations between topology and the quantum metric for Chern insulators. Phys. Rev. B, 104:045103, Jul 2021. [2] Bruno Mera and Tomoki Ozawa. Kähler geometry and Chern insulators: Relations between topology and the quantum metric. Phys. Rev. B, 104:045104, Jul 2021. [3] Bruno Mera and Tomoki Ozawa. Engineering geometrically flat Chern bands with Fubini-Study Kähler structure. Phys. Rev. B, 104:115160, Sep 2021.
| 27 | 28 - CMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Algebraic Geometry in String Theory Seminar**Speaker: Ahsan Khan, IAS - Member Seminar: Title TBACMSA, 20 Garden Street, Cambridge, MA 02138 USA
**Speaker:**Shuaijie Qian
| 29 |

30 | 31 | November | November | November | November | November |