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DTSTART;TZID=America/New_York:20220928T140000
DTEND;TZID=America/New_York:20220928T150000
DTSTAMP:20240214T110335Z
CREATED:20230808T184138Z
LAST-MODIFIED:20240214T110335Z
UID:10001211-1664373600-1664377200@cmsa.fas.harvard.edu
SUMMARY:Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling
DESCRIPTION:New Technologies in Mathematics \nSpeaker: Surya Ganguli\, Stanford University \n\nTitle: Statistical mechanics of neural networks: From the geometry of high dimensional error landscapes to beating power law neural scaling\n\n\n\n\nAbstract: 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.\n\n\n\nReferences: 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.\n\nSorscher\, 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).
URL:https://cmsa.fas.harvard.edu/event/8303/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-09.28.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20220930T110000
DTEND;TZID=America/New_York:20220930T120000
DTSTAMP:20240301T081921Z
CREATED:20240214T105247Z
LAST-MODIFIED:20240301T081921Z
UID:10002683-1664535600-1664539200@cmsa.fas.harvard.edu
SUMMARY:Kahler geometry in twisted materials
DESCRIPTION:Member Seminar \nSpeaker: Jie Wang \nTitle: Kahler geometry in twisted materials \nAbstract: 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. \nIn 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.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-93022/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221005T140000
DTEND;TZID=America/New_York:20221005T160000
DTSTAMP:20240214T110102Z
CREATED:20230808T184616Z
LAST-MODIFIED:20240214T110102Z
UID:10001212-1664978400-1664985600@cmsa.fas.harvard.edu
SUMMARY:Minerva: Solving Quantitative Reasoning Problems with Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Guy Gur-Ari\, Google Research \nTitle: Minerva: Solving Quantitative Reasoning Problems with Language Models \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/minerva-solving-quantitative-reasoning-problems-with-language-models/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/10.05.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221005T160000
DTEND;TZID=America/New_York:20221005T170000
DTSTAMP:20240229T110447Z
CREATED:20230817T173038Z
LAST-MODIFIED:20240229T110447Z
UID:10001266-1664985600-1664989200@cmsa.fas.harvard.edu
SUMMARY:Quantum statistical mechanics of charged black holes and strange metals
DESCRIPTION:Colloquium \nPlease note this colloquium will be held at a special time:  4:00-5:00 pm. \nSpeaker: Subir Sachdev (Harvard) \nTitle: Quantum statistical mechanics of charged black holes and strange metals\n\nAbstract: 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.\n\n\nSlides: cmsa22
URL:https://cmsa.fas.harvard.edu/event/colloquium_10522/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.05.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221007T110000
DTEND;TZID=America/New_York:20221007T120000
DTSTAMP:20240301T081713Z
CREATED:20240214T105028Z
LAST-MODIFIED:20240301T081713Z
UID:10002681-1665140400-1665144000@cmsa.fas.harvard.edu
SUMMARY:Principal flow\, sub-manifold and boundary
DESCRIPTION:Member Seminar  \nSpeaker: Zhigang Yao \nTitle: Principal flow\, sub-manifold and boundary \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-10722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221012T123000
DTEND;TZID=America/New_York:20221012T133000
DTSTAMP:20240222T165414Z
CREATED:20230817T173346Z
LAST-MODIFIED:20240222T165414Z
UID:10001267-1665577800-1665581400@cmsa.fas.harvard.edu
SUMMARY:Complete disorder is impossible: Some topics in Ramsey theory
DESCRIPTION:Colloquium \nSpeaker: James Cummings\,Carnegie Mellon University \nTitle: Complete disorder is impossible: Some topics in Ramsey theory \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/collquium-101222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.12.22-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221014T110000
DTEND;TZID=America/New_York:20221014T120000
DTSTAMP:20240301T081027Z
CREATED:20240214T103536Z
LAST-MODIFIED:20240301T081027Z
UID:10002676-1665745200-1665748800@cmsa.fas.harvard.edu
SUMMARY:Quantum magnet chains and Kashiwara crystals
DESCRIPTION:Speaker: Leonid Rybnikov\, Harvard CMSA/National Research University Higher School of Economics \nTitle: Quantum magnet chains and Kashiwara crystals \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-101422/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.14.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221019T123000
DTEND;TZID=America/New_York:20221019T133000
DTSTAMP:20240214T113414Z
CREATED:20230817T173735Z
LAST-MODIFIED:20240214T113414Z
UID:10001268-1666182600-1666186200@cmsa.fas.harvard.edu
SUMMARY:The Mobility Edge of Lévy Matrices
DESCRIPTION:Colloquium \nSpeaker: Patrick Lopatto (Brown) \nTitle: The Mobility Edge of Lévy Matrices \nAbstract: Lévy matrices are symmetric random matrices whose entry distributions lie in the domain of attraction of an alpha-stable law; such distributions have infinite variance when alpha is less than 2. Due to the ubiquity of heavy-tailed randomness\, these models have been broadly applied in physics\, finance\, and statistics. When the entries have infinite mean\, Lévy matrices are predicted to exhibit a phase transition separating a region of delocalized eigenvectors from one with localized eigenvectors. We will discuss the physical context for this conjecture\, and describe a result establishing it for values of alpha close to zero and one. This is joint work with Amol Aggarwal and Charles Bordenave.
URL:https://cmsa.fas.harvard.edu/event/collquium-101922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.19.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221019T140000
DTEND;TZID=America/New_York:20221019T150000
DTSTAMP:20240215T095357Z
CREATED:20230808T184955Z
LAST-MODIFIED:20240215T095357Z
UID:10001213-1666188000-1666191600@cmsa.fas.harvard.edu
SUMMARY:Towards Faithful Reasoning Using Language Models
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Antonia Creswell\, DeepMind \nTitle: Towards Faithful Reasoning Using Language Models \nAbstract: Language models are showing impressive performance on many natural language tasks\, including question-answering. However\, language models – like most deep learning models – are black boxes. We cannot be sure how they obtain their answers. Do they reason over relevant knowledge to construct an answer or do they rely on prior knowledge – baked into their weights – which may be biased? An alternative approach is to develop models whose output is a human interpretable\, faithful reasoning trace leading to an answer. In this talk we will characterise faithful reasoning in terms of logically valid reasoning and demonstrate where current reasoning models fall short. Following this\, we will introduce Selection-Inference\, a faithful reasoning model\, whose causal structure mirrors the requirements for valid reasoning. We will show that our model not only produces more accurate reasoning traces but also improves final answer accuracy. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/nt-101922/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/10.19.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221021T110000
DTEND;TZID=America/New_York:20221021T120000
DTSTAMP:20240301T080144Z
CREATED:20230809T110107Z
LAST-MODIFIED:20240301T080144Z
UID:10001226-1666350000-1666353600@cmsa.fas.harvard.edu
SUMMARY:Explicit Ramsey Graphs and Two Source Extractors
DESCRIPTION:Speaker: David Zuckerman\, Harvard CMSA/University of Texas at Austin \nTitle: Explicit Ramsey Graphs and Two Source Extractors \nAbstract: Ramsey showed that any graph on N nodes contains a clique or independent set of size (log N)/2.  Erdos showed that there exist graphs on N nodes with no clique or independent set of size 2 log N\, and asked for an explicit construction of such graphs.  This turns out to relate to the question of extracting high-quality randomness from two independent low-quality sources.  I’ll explain this connection and our recent exponential improvement in constructing two-source extractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-5/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-10.21.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221026T123000
DTEND;TZID=America/New_York:20221026T133000
DTSTAMP:20240121T174027Z
CREATED:20230817T174027Z
LAST-MODIFIED:20240121T174027Z
UID:10001269-1666787400-1666791000@cmsa.fas.harvard.edu
SUMMARY:Clique listing algorithms
DESCRIPTION:Speaker: Virginia Vassilevska Williams (MIT) \nTitle: Clique listing algorithms \nAbstract: A k-clique in a graph G is a subgraph of G on k vertices in which every pair of vertices is linked by an edge. Cliques are a natural notion of social network cohesiveness with a long history. \nA fundamental question\, with many applications\, is “How fast can one list all k-cliques in a given graph?”. \nEven just detecting whether an n-vertex graph contains a k-Clique has long been known to be NP-complete when k can depend on n (and hence no efficient algorithm is likely to exist for it). If k is a small constant\, such as 3 or 4 (independent of n)\, even the brute-force algorithm runs in polynomial time\, O(n^k)\, and can list all k-cliques in the graph; though O(n^k) time is far from practical. As the number of k-cliques in an n-vertex graph can be Omega(n^k)\, the brute-force algorithm is in some sense optimal\, but only if there are Omega(n^k) k-cliques. In this talk we will show how to list k-cliques faster when the input graph has few k-cliques\, with running times depending on the number of vertices n\, the number of edges m\, the number of k-cliques T and more. We will focus on the case when k=3\, but we will note some extensions. \n(Based on joint work with Andreas Bjorklund\, Rasmus Pagh\, Uri Zwick\, Mina Dalirrooyfard\, Surya Mathialagan and Yinzhan Xu)
URL:https://cmsa.fas.harvard.edu/event/collquium_102722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-10.26.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221026T140000
DTEND;TZID=America/New_York:20221026T150000
DTSTAMP:20240115T103149Z
CREATED:20230808T185319Z
LAST-MODIFIED:20240115T103149Z
UID:10001214-1666792800-1666796400@cmsa.fas.harvard.edu
SUMMARY:From Engine to Auto
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeakers: João Araújo\, Mathematics Department\, Universidade Nova de Lisboa and Michael Kinyon\, Department of Mathematics\, University of Denver \n\nTitle: From Engine to Auto \n\n\nAbstract: Bill McCune produced the program EQP that deals with first order logic formulas and in 1996 managed to solve Robbins’ Conjecture. This very powerful tool reduces to triviality any result that can be obtained by encoding the assumptions and the goals. The next step was to turn the program into a genuine assistant for the working mathematician: find ways to help the prover with proofs; reduce the lengths of the automatic proofs to better crack them;  solve problems in higher order logic; devise tools that autonomously prove results of a given type\, etc.\n\nIn this talk we are going to show some of the tools and strategies we have been producing. There will be real illustrations of theorems obtained for groups\, loops\, semigroups\, logic algebras\, lattices and generalizations\, quandles\, and many more.
URL:https://cmsa.fas.harvard.edu/event/nt-102622/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-NTM-Seminar-10.26.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221028T110000
DTEND;TZID=America/New_York:20221028T120000
DTSTAMP:20240301T080243Z
CREATED:20230809T110603Z
LAST-MODIFIED:20240301T080243Z
UID:10001227-1666954800-1666958400@cmsa.fas.harvard.edu
SUMMARY:Some non-concave dynamic optimization problems in finance
DESCRIPTION:Member Seminar \nSpeaker: Shuaijie Qian (Harvard CMSA) \nTitle: Some non-concave dynamic optimization problems in finance \nAbstract: Non-concave dynamic optimization problems appear in many areas of finance and economics. Most of existing literature solves these problems using the concavification principle\, and derives equivalent\, concave optimization problems whose value functions are still concave. In this talk\, I will present our recent work on some non-concave dynamic optimization problems\, where the concavification principle may not hold and the resulting value function is indeed non-concave. \nThe first work is about the portfolio selection model with capital gains tax and a bitcoin mining model with exit options and technology innovation\, where the average tax basis and the average mining cost serves as an approximation\, respectively. This approximation results in a non-concave value function\, and the associated HJB equation problem turns out to admit infinitely many solutions. We show that the value function is the minimal (viscosity) solution of the HJB equation problem. Moreover\, the penalty method still works and converges to the value function. \nThe second work is about a non-concave utility maximization problem with portfolio constraints. We find that adding bounded portfolio constraints\, which makes the concavification principle invalid\, can significantly affect economic insights in the existing literature. As the resulting value function is likely discontinuous\, we introduce a new definition of viscosity solution\, prove the corresponding comparison principle\, and show that a monotone\, stable\, and consistent finite difference scheme converges to the solution of the utility maximization problem. \n 
URL:https://cmsa.fas.harvard.edu/event/member-seminar-title-tba-6/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221102T124500
DTEND;TZID=America/New_York:20221102T134500
DTSTAMP:20240121T174258Z
CREATED:20230817T174336Z
LAST-MODIFIED:20240121T174258Z
UID:10001270-1667393100-1667396700@cmsa.fas.harvard.edu
SUMMARY:Doping and inverting Mott insulators on semiconductor moire superlattices
DESCRIPTION:Speaker: Liang Fu (MIT) \n\n\nTitle: Doping and inverting Mott insulators on semiconductor moire superlattices \nAbstract: Semiconductor bilayer heterostructures provide a remarkable platform for simulating Hubbard models on an emergent lattice defined by moire potential minima. As a hallmark of Hubbard model physics\, the Mott insulator state with local magnetic moments has been observed at half filling of moire band. In this talk\, I will describe new phases of matter that grow out of the canonical 120-degree antiferromagnetic Mott insulator on the triangular lattice. First\, in an intermediate range of magnetic fields\, doping this Mott insulator gives rise to a dilute gas of spin polarons\, which form a pseudogap metal. Second\, the application of an electric field between the two layers can invert the many-body gap of a charge-transfer Mott insulator\, resulting in a continuous phase transition to a quantum anomalous Hall insulator with a chiral spin structure. Experimental results will be discussed and compared with theoretical predictions.
URL:https://cmsa.fas.harvard.edu/event/collquium-11222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.02.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221111T110000
DTEND;TZID=America/New_York:20221111T120000
DTSTAMP:20240209T052938Z
CREATED:20230809T111328Z
LAST-MODIFIED:20240209T052938Z
UID:10001228-1668164400-1668168000@cmsa.fas.harvard.edu
SUMMARY:Quantum trace and length conjecture for hyperbolic knot
DESCRIPTION:Member Seminar \nSpeaker: Mauricio Romo \nTitle: Quantum trace and length conjecture for hyperbolic knot \nAbstract: I will define the quantum trace map for an ideally triangulated hyperbolic knot complement on S^3. This map assigns an operator to each element L of  the Kauffman Skein module of knot complement.  Motivated by an interpretation of this operator in the context of SL(2\,C) Chern-Simons theory\, one can formulate a ‘length conjecture’ for the hyperbolic length of L.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111122/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221116T123000
DTEND;TZID=America/New_York:20221116T133000
DTSTAMP:20240214T112838Z
CREATED:20230817T174642Z
LAST-MODIFIED:20240214T112838Z
UID:10001271-1668601800-1668605400@cmsa.fas.harvard.edu
SUMMARY:Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks
DESCRIPTION:Colloquium \nSpeaker: Hidenori Tanaka (NTT Research at Harvard) \nTitle: Noether’s Learning Dynamics: Role of Symmetry Breaking in Neural Networks \nAbstract: In nature\, symmetry governs regularities\, while symmetry breaking brings texture. In artificial neural networks\, symmetry has been a central design principle\, but the role of symmetry breaking is not well understood. Here\, we develop a Lagrangian formulation to study the geometry of learning dynamics in neural networks and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. Then\, we generalize Noether’s theorem known in physics to describe a unique symmetry breaking mechanism in learning and derive the resulting motion of the Noether charge: Noether’s Learning Dynamics (NLD). Finally\, we apply NLD to neural networks with normalization layers and discuss practical insights. Overall\, through the lens of Lagrangian mechanics\, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.
URL:https://cmsa.fas.harvard.edu/event/collquium-111622/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-11.16.22-2.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221118T110000
DTEND;TZID=America/New_York:20221118T120000
DTSTAMP:20240209T052933Z
CREATED:20230809T111725Z
LAST-MODIFIED:20240209T052933Z
UID:10001229-1668769200-1668772800@cmsa.fas.harvard.edu
SUMMARY:Light states in the interior of CY moduli spaces
DESCRIPTION:Member Seminar \nSpeaker: Damian van de Heisteeg \nTitle: Light states in the interior of CY moduli spaces \nAbstract: In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction\, that is\, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points\, and find that they correspond to special points in the moduli space of the CY\, such as orbifold points and rank two attractors.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-111822/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-11.18.22.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221202T110000
DTEND;TZID=America/New_York:20221202T120000
DTSTAMP:20240229T111029Z
CREATED:20230817T164654Z
LAST-MODIFIED:20240229T111029Z
UID:10001230-1669978800-1669982400@cmsa.fas.harvard.edu
SUMMARY:Compactness and Anticompactness Principles in Set Theory
DESCRIPTION:Member Seminar \nSpeaker: Alejandro Poveda \nTitle: Compactness and Anticompactness Principles in Set Theory \nAbstract: Several fundamental properties in Topology\, Algebra or Logic are expressed in terms of Compactness Principles.For instance\, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise\, we say that compactness fails. Loosely speaking\, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group\, a topological space\, etc) such that all of its small substructures N have certain property $\varphi$; then the ambient structure M has property $\varphi$\, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits\, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-12222/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20221207T140000
DTEND;TZID=America/New_York:20221207T150000
DTSTAMP:20240116T060930Z
CREATED:20230808T185642Z
LAST-MODIFIED:20240116T060930Z
UID:10001215-1670421600-1670425200@cmsa.fas.harvard.edu
SUMMARY:How do Transformers reason? First principles via automata\, semigroups\, and circuits
DESCRIPTION:New Technologies in Mathematics Seminar \nSpeaker: Cyril Zhang\, Microsoft Research \nTitle: How do Transformers reason? First principles via automata\, semigroups\, and circuits \nAbstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models\, leading to dramatic advances in natural language understanding\, program synthesis\, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses\, given that they resist interpretation? In this work\, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure. \nSpecifically\, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory\, we characterize shortcut solutions\, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore\, in synthetic experiments\, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness\, and discuss mitigations. \nJoint work with Bingbin Liu\, Jordan Ash\, Surbhi Goel\, and Akshay Krishnamurthy.
URL:https://cmsa.fas.harvard.edu/event/nt-12722/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:New Technologies in Mathematics Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/12.07.2022.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230131T120000
DTEND;TZID=America/New_York:20230131T130000
DTSTAMP:20240118T033236Z
CREATED:20230817T164947Z
LAST-MODIFIED:20240118T033236Z
UID:10001231-1675166400-1675170000@cmsa.fas.harvard.edu
SUMMARY:AI and Theorem Proving
DESCRIPTION:Member Seminar \nSpeaker: Mike Douglas \nTitle: AI and Theorem Proving \nAbstract: We survey interactive theorem proving and the Lean theorem prover\, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-13123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230202T123000
DTEND;TZID=America/New_York:20230202T133000
DTSTAMP:20240121T174936Z
CREATED:20230817T175011Z
LAST-MODIFIED:20240121T174936Z
UID:10001272-1675341000-1675344600@cmsa.fas.harvard.edu
SUMMARY:Neural Optimal Stopping Boundary
DESCRIPTION:Speaker: Max Reppen (Boston University) \nTitle: Neural Optimal Stopping Boundary \nAbstract:  A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments\, some in high dimensions\, are analyzed through this method\, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.
URL:https://cmsa.fas.harvard.edu/event/colloquium_2223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-02.02.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230207T120000
DTEND;TZID=America/New_York:20230207T130000
DTSTAMP:20240215T101240Z
CREATED:20230817T165237Z
LAST-MODIFIED:20240215T101240Z
UID:10001232-1675771200-1675774800@cmsa.fas.harvard.edu
SUMMARY:Motivic Geometry of Two-Loop Feynman Integrals
DESCRIPTION:Member Seminar \nSpeaker: Chuck Doran \nTitle: Motivic Geometry of Two-Loop Feynman Integrals \nAbstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves\, elliptic curves\, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular\, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves\, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly\, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-2723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230208T123000
DTEND;TZID=America/New_York:20230208T133000
DTSTAMP:20240214T112702Z
CREATED:20230817T175326Z
LAST-MODIFIED:20240214T112702Z
UID:10001273-1675859400-1675863000@cmsa.fas.harvard.edu
SUMMARY:From spin glasses to Boolean circuits lower bounds - Algorithmic barriers from the overlap gap property
DESCRIPTION:Speaker: David Gamarnik (MIT) \nTitle: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property \nAbstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph\, the problem of finding a near ground state in a spin glass model\, the problem of finding a satisfying assignment in a random constraint satisfaction problem\, and many many more. Unfortunately\, at the same time no formal computational hardness results exist which  explains this persistent algorithmic gap. \nIn the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses\, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and\, importantly\, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders\, specifically the algorithms which exhibit a form of stability/noise insensitivity. \nWe will specifically show how to use this property to obtain stronger (stretched exponential) than the state of the art (quasi-polynomial) lower bounds on the size of constant depth Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph\, and the problem of finding a near ground state of a p-spin model. \nJoint work with Aukosh Jagannath and Alex Wein
URL:https://cmsa.fas.harvard.edu/event/collquium-2823/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-02.08.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230213T123000
DTEND;TZID=America/New_York:20230213T133000
DTSTAMP:20240222T165748Z
CREATED:20230817T175704Z
LAST-MODIFIED:20240222T165748Z
UID:10001274-1676291400-1676295000@cmsa.fas.harvard.edu
SUMMARY:Complete Calabi-Yau metrics: Recent progress and open problems
DESCRIPTION:Speaker: Tristan Collins\, MIT \nTitle: Complete Calabi-Yau metrics: Recent progress and open problems \nAbstract: Complete Calabi-Yau metrics are fundamental objects in Kahler geometry arising as singularity models or “bubbles” in degenerations of compact Calabi-Yau manifolds.  The existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to Yau and Tian-Yau. I will describe some recent progress towards the question of existence\, and explain some future directions\, highlighting connections with notions of algebro-geometric stability.
URL:https://cmsa.fas.harvard.edu/event/collquium-21323/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-02.13.2023-.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230214T120000
DTEND;TZID=America/New_York:20230214T130000
DTSTAMP:20240228T094059Z
CREATED:20230817T165432Z
LAST-MODIFIED:20240228T094059Z
UID:10001233-1676376000-1676379600@cmsa.fas.harvard.edu
SUMMARY:Dynamics of active nematic defects on cones
DESCRIPTION:Member Seminar \nSpeaker: Farzan Vafa \nTitle: Dynamics of active nematic defects on cones \nAbstract: In the first part of the talk\, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge\, which in analogy to electrostatics\, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle\, which is determined by charged defects screening the effective apex charge: (i) for sharp cones\, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles\, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones\, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk\, we investigate the dynamics of an active nematic on a cone\, and via simulations find long-time circular orbits of either one or two flank defects\, with transitions between these states mediated by the apex via defect absorption\, emission\, or defect pair creation.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-21423/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230221T120000
DTEND;TZID=America/New_York:20230221T130000
DTSTAMP:20240118T052804Z
CREATED:20230817T165641Z
LAST-MODIFIED:20240118T052804Z
UID:10001234-1676980800-1676984400@cmsa.fas.harvard.edu
SUMMARY:Hints of Flat Space Holography
DESCRIPTION:Member Seminar \nSpeaker: Dan Kapec \nTitle: Hints of Flat Space Holography \nAbstract: Despite our detailed understanding of holography in Anti-de Sitter space\, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space\, bulk gravitons produce a boundary stress tensor\, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-22123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230222T123000
DTEND;TZID=America/New_York:20230222T133000
DTSTAMP:20240215T111058Z
CREATED:20230817T180053Z
LAST-MODIFIED:20240215T111058Z
UID:10001275-1677069000-1677072600@cmsa.fas.harvard.edu
SUMMARY:The Black Hole Information Paradox: A Resolution on the Horizon?
DESCRIPTION:Speaker: Netta Engelhardt (MIT) \nTitle: The Black Hole Information Paradox: A Resolution on the Horizon? \nAbstract: The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary\, and in particular its application to entanglement and complexity\, however\, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.
URL:https://cmsa.fas.harvard.edu/event/collquium-22223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-02.22.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230302T120000
DTEND;TZID=America/New_York:20230302T130000
DTSTAMP:20240118T052933Z
CREATED:20230817T165840Z
LAST-MODIFIED:20240118T052933Z
UID:10001235-1677758400-1677762000@cmsa.fas.harvard.edu
SUMMARY:New bounds on lattice covering volumes\, and nearly uniform covers
DESCRIPTION:Member Seminar \nSpeaker: Barak Weiss   \nTitle: New bounds on lattice covering volumes\, and nearly uniform covers \nAbstract: Let L be a lattice in R^n and let K be a convex body. The covering volume of L with respect to K is the minimal volume of a dilate rK\, such that L+rK = R^n\, normalized by the covolume of L. Pairs (L\,K) with small covering volume correspond to efficient coverings of space by translates of K\, where the translates lie in a lattice. Finding upper bounds on the covering volume as the dimension n grows is a well studied problem\, with connections to practical questions arising in computer science and electrical engineering. In a recent paper with Or Ordentlich (EE\, Hebrew University) and Oded Regev (CS\, NYU) we obtain substantial improvements to bounds of Rogers from the 1950s. In another recent paper\, we obtain bounds on the minimal volume of nearly uniform covers (to be defined in the talk). The key to these results are recent breakthroughs by Dvir and others regarding the discrete Kakeya problem. I will give an overview of the questions and results.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-3223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230302T160000
DTEND;TZID=America/New_York:20230302T170000
DTSTAMP:20240216T085143Z
CREATED:20230817T180503Z
LAST-MODIFIED:20240216T085143Z
UID:10001276-1677772800-1677776400@cmsa.fas.harvard.edu
SUMMARY:The string/black hole transition in anti de Sitter space
DESCRIPTION:Speaker: Erez Urbach\, Weizmann Institute of Science \nTitle: The string/black hole transition in anti de Sitter space \nAbstract: String stars\, or Horowitz-Polchinski solutions\, are string theory saddles with normalizable condensates of thermal-winding strings. In the past\, string stars were offered as a possible description of stringy (Euclidean) black holes in asymptotically flat spacetime\, close to the Hagedorn temperature. I will discuss the thermodynamic properties of string stars in asymptotically (thermal) anti-de Sitter background (including AdS3 with NS-NS flux)\, their possible connection to small black holes in AdS\, and their implications for holography. I will also present new “winding-string gas” saddles for confining holographic backgrounds such as the Witten model\, and their relation to the deconfined phase of 3+1 pure Yang-Mills.
URL:https://cmsa.fas.harvard.edu/event/collquium-3223/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/02CMSA-Colloquium-03.02.2023.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230307T120000
DTEND;TZID=America/New_York:20230307T130000
DTSTAMP:20240118T064352Z
CREATED:20230817T170153Z
LAST-MODIFIED:20240118T064352Z
UID:10001236-1678190400-1678194000@cmsa.fas.harvard.edu
SUMMARY:Categorical Symmetry of the Standard Model from Gravitational Anomaly 
DESCRIPTION:Member Seminar \nSpeaker: Juven Wang \nTitle: Categorical Symmetry of the Standard Model from Gravitational Anomaly \nAbstract: In the Standard Model\, the total “sterile right-handed” neutrino number n_{νR} is not equal to the family number Nf. The anomaly index (-Nf+n_{νR}) had been advocated to play an important role in our previous work on Cobordism and Deformation Class of the Standard Model [2112.14765\, 2204.08393] and Ultra Unification [2012.15860] in order to predict new highly entangled sectors beyond the Standard Model. Moreover\, the invertible baryon minus lepton number B−L symmetry current conservation can be violated quantum mechanically by gravitational backgrounds such as gravitational instantons. In specific\, we show that a noninvertible categorical counterpart of the B−L symmetry still survives in gravitational backgrounds. In general\, we propose a construction of noninvertible symmetry charge operators as topological defects derived from invertible anomalous symmetries that suffer from mixed gravitational anomalies. Examples include the perturbative local and nonperturbative global anomalies classified by ℤ and ℤ16 respectively. For this construction\, we utilize the anomaly inflow concept and the 3d Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding to a 2d rational conformal field theory with an appropriate chiral central charge\, or the 3d boundary topological order of 4d ℤTF4-time-reversal symmetric topological superconductor [2302.14862].
URL:https://cmsa.fas.harvard.edu/event/member-seminar-3723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
END:VEVENT
END:VCALENDAR