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September  September  September  September  September  September  1 
2  3  4  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics: Holomorphic Twists and Confinement in N=1 SYM
9:30 AM11:00 AM October 4, 2022
Supersymmetric QFT’s are of longstanding 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 KacMoody 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 YangMills. Based on arXiv:2207.14321 and 2 forthcoming works with Kasia Budzik, Davide Gaiotto, Brian Williams, Jingxiang Wu, and Matthew Yu.
For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantummatterseminar/  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM October 4, 2022 1 Oxford Street, Cambridge, MA 02138 USA
I will discuss my ongoing effort to comprehend, from a geometric viewpoint, the motivic monodromy conjecture for a “generic” complex multivariate polynomial f, namely any polynomial f that is nondegenerate with respect to its Newton polyhedron. This conjecture, due to Igusa and Denef–Loeser, states that for every pole s of the motivic zeta function associated to f, exp(2πis) is a “monodromy eigenvalue” associated to f. On the other hand, the nondegeneracy condition on f ensures that the singularity theory of f is governed, up to a certain extent, by faces of the Newton polyhedron of f. The extent to which the former is governed by the latter is one key aspect of the conjecture, and will be the main focus of my talk.
 5  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Dynamic control of slow processes – quantum annealing, cold thermalization and coarsening
9:00 AM10:00 AM October 5, 2022 1 Oxford Street, Cambridge, MA 02138 USA
This talk will start by reviewing the basic physics of slow collective tunnelling and its relevance to adiabatic quantum computation (AQC). We then focus on the recently introduced dynamic protocols that stabilize AQC against control errors (following https://iopscience.iop.org/article/10.1088/20589565/abd59a). Recent unpublished work applying these ideas to conventional ordered states, e.g. quantum ferromagnets, will also be presented.
 CMSA EVENT: CMSA New Technologies in Mathematics: Minerva: Solving Quantitative Reasoning Problems with Language Models
2:00 PM3:00 PM October 5, 2022 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 transformerbased language models obtain significantly better performance on math and science questions when trained in an unsupervised way on a large, mathfocused dataset. Performance can be further improved using prompting and sampling techniques including chainofthought 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.
For more information, please see: https://cmsa.fas.harvard.edu/techinmath/  NUMBER THEORY SEMINAR
3:00 PM4:00 PM October 5, 2022 1 Oxford Street, Cambridge, MA 02138 USA The Langlands program predicts a relationship between automorphic representations of a reductive group G and Galois representations valued in its Lgroup. For general G over a global function field, the automorphictoGalois direction has been constructed by V. Lafforgue. More recently, for general G over a nonarchimedean local field, a similar correspondence has been constructed by Fargues–Scholze. We present a proof that the V. Lafforgue and Fargues–Scholze correspondences are compatible, generalizing localglobal compatibility from class field theory. As a consequence, the correspondences of Genestier–Lafforgue and Fargues–Scholze agree, which answers a question of Fargues–Scholze, Hansen, Harris, and Kaletha.  SEMINARS
4:00 PM5:00 PM October 5, 2022  CMSA EVENT: CMSA Colloquium: Quantum statistical mechanics of charged black holes and strange metals
4:00 PM5:00 PM October 5, 2022 1 Oxford Street, Cambridge, MA 02138 USA
The SachdevYeKitaev model was introduced as a toy model of interacting fermions without any particlelike 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  OTHER MATHEMATICS DEPARTMENT EVENTS
4:30 PM6:00 PM October 6, 2022 Math is more than just a way to describe the world, and it is more than just a set of skills, like doing arithmetic and factoring a quadratic. Math is a deeply human enterprise that fulfills basic human longings, such as for beauty and truth. When properly engaged, it builds virtues like persistence, creativity, and a competence to solve new problems. These virtues will serve you well no matter what you do in life. It was an incarcerated man–now his friend–that helped distinguished mathematician Francis Su see this more clearly than ever before.
 7  CMSA EVENT: CMSA Algebraic Geometry in String Theory: Scattering Diagrams from Holomorphic Discs in Log Calabi–Yau Surfaces
9:30 AM10:30 AM October 7, 2022 20 Garden Street, Cambridge, MA 02138
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 algebrogeometric 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 GromovWitten invariants. This talk is based on joint work with ManWai Mandy Cheung, Hansol Hong, and YuShen Lin.
For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/algebraicgeometryinstringtheory/  SEMINARS
3:30 PM4:30 PM October 7, 2022 1 Oxford Street, Cambridge, MA 02138 USA
We will talk about our recent construction of the smallest closed exotic 4manifolds with signature zero known to date. Our novel examples are derived from fairly special small Lefschetz fibrations we build, with spin and nonspin monodromies. This is joint work with N. Hamada.
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9  10  11  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR
3:00 PM4:00 PM October 11, 2022 1 Oxford Street, Cambridge, MA 02138 USA
The minimal model program is an ambitious program that aims to understand the geometry of complex projective varieties (eg. manifolds defined by polynomial equations). In this talk we will discuss some recent results and challenges encountered trying to extend the minimal model program to the context of Kähler varieties.
 12  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Engineering topological phases with a superlattice potential
9:00 AM10:00 AM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA
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 spinorbit coupling and Coulomb repulsion give rise to a topological meron lattice spin texture. Thus, the superlattice potential provides a new route to the long soughtafter 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 Bernalstacked 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.
 NUMBER THEORY SEMINAR
3:00 PM4:00 PM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA  OPEN NEIGHBORHOOD SEMINAR
4:30 PM5:30 PM October 12, 2022 1 Oxford Street, Cambridge, MA 02138 USA
 13  SEMINARS
4:00 PM6:00 PM October 13, 2022
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16  17  OTHER MATHEMATICS DEPARTMENT EVENTS
3:00 PM6:00 PM October 17, 2022 1 Oxford Street, Cambridge, MA 02138 USA Jameel AlAidroos was a treasured colleague and a master of a myriad of things. He could simplify a mathematical idea and present a question or comment in a way that could bring his students to view concepts from new perspectives. Likewise, when he worked with graduate students around pedagogy and with school teachers around the joys of engaging with mathematics, the thoughtful way he approached teaching and mentorship made a big difference. Watching Jameel teach motivated and inspired both novice and veteran teachers to become better instructors and to bring their best selves forward. His superpower as a teacher was asking just the right questions to focus students’ attention on the core of the mathematical idea. Through a number of seminars and workshops, Jameel shared his questionasking approach and pedagogical skills with graduate students and faculty. An astute and careful listener, a masterful communicator, and a deep thinker, he forged impactful connections. As a mentor and colleague, Jameel was without equal: he applied himself wholeheartedly to hone his craft in the classroom and as a mentor. He was quick to volunteer to do whatever was needed to promote team projects and through this, we discovered his enormous talents as an interviewer, film editor, and voiceover artist, among other things. It seemed there were no tasks he did not choose to rise to and polish, while consistently taking a step out of the limelight to let his students and colleagues shine. The grace and generosity of spirit he extended to his students and colleagues are an indelible part of his legacy. Jameel carried this grace and generosity throughout his long battle with cancer. We honor his contributions and dedication to teaching and learning at Harvard via this speaker series as a small way to remember Jameel’s extraordinary warmth of character and pedagogical skills. He motivated and inspired his students and colleagues; through this series, we hope to celebrate and keep alive that legacy by bringing speakers who share new perspectives on mathematics and pedagogy, and motivate us to reflect on our professional roles. Jameel AlAidroos Mathematical Pedagogy Lecture Series When: October 17, 2022 Where: Hall E, Science Center, 1 Oxford Street, Cambridge, MA, 02138 Register for the InPerson Event. Register for the Online Event. Download a detailed PDF schedule of lectures and events. Schedule 

3 p.m. – 3:50 p.m. Aubrey Clayton  Author of Bernoulli’s Fallacy: Statistical Illogic and the Crisis of Modern Science Thinking Slowly about Probability and Statistics  3:50 p.m. – 4 p.m. Break  4 p.m. – 4:50 p.m. Juliana Belding  Associate Professor of the Practice of Mathematics at Boston College Working with Secondary Math Teachers: What Mathematicians can Offer and Learn  5 p.m. – 6 p.m. Refreshments in The Austine & Chilton McDonnell Common Room, Science Center 4th floor. 
Organizers
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23  24  25  26  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Kähler bands—Chern insulators, holomorphicity and induced quantum geometry
9:00 AM10:00 AM October 26, 2022 1 Oxford Street, Cambridge, MA 02138 USA
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 momentumspace 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 constrains, 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 translationinvariant (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 wellknown 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.
 NUMBER THEORY SEMINAR
3:00 PM4:00 PM October 26, 2022 1 Oxford Street, Cambridge, MA 02138 USA
The usual language of algebraic geometry is not appropriate for arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace s rings by the collection of “vectors” or by bioperads, and another based on “matrices” or props. Once one understands the delicate commutativity condition one can proceed following Grothendieck’s footsteps exactly. The props, when viewed up to conjugation, give us new commutative rings with Frobenius endomorphisms.
 27  SEMINARS
4:00 PM6:00 PM October 27, 2022
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30  31  November  November  November  November  November 