
Sun  Mon  Tue  Wed  Thu  Fri  Sat 

August  August  August  August  August  1  CMSA EVENT: CMSA CONFERENCE ON BIG DATA
All day September 1, 2023September 1, 2023 ***** On August 31–Sep 1, 2023 the CMSA will host the ninth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe, with talks focusing on computer science, statistics, math and physics, and economics. For more information, please see: https://cmsa.fas.harvard.edu/event/bigdata_2023/ *****
 2 
3  4  5  SEMINARS: Mathematical Picture Language Seminar: Equivalence Principle, DeSitter Space, and Twistor Theory
Speaker: Maciej Dunajski – University of Cambridge 9:30 AM10:30 AM September 5, 2023 I discuss the impact of the positive cosmological constant on the interplay between the equivalence principle in general relativity, and the rules of quantum mechanics. There is an ambiguity in the definition of a phase of a wave function measured by inertial and accelerating observes which is a nonrelativistic analogue of the Unruh effect. This will be put in the framework of a nonrelativistic limit of twistor space.
 6  SEMINARS: Combinatorics Seminar: Size of the largest sumfree subset of [n]^3
Speaker: Saba Lepsveride & Yihang “Kimi” Sun – MIT 4:15 PM6:00 PM September 6, 2023
We prove a conjecture by Cameron and Aydinian in three dimensions, showing that the density of the largest sumfree subset of [n]^3 approaches (10 + √15)/20 as n approaches infinity. The resolution of the twodimensional problem was accomplished by Elsholtz and Rackham in 2017. In this work, we introduce a different approach that involves considering a relaxed linear program on the projection [n]^2 and then constructing a suitable dual solution. We also explore potential approaches for addressing the higherdimensional version of this problem. For information about the Combinatorics Seminar, please visit http://math.mit.edu/seminars/combin/
 7  CMSA EVENT: CMSA Probability Seminar: Correlation decay for finite lattice gauge theories
Speaker: Arka Adhikari – Stanford University 1:30 PM2:30 PM September 7, 2023
In the setting of lattice gauge theories with finite (possibly nonAbelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.  COLLOQUIUMS: Special Colloquium – Systems of points with Coulomb interactions
Speaker: Sylvia Serfaty – NYU Courant Institute 3:00 PM4:00 PM September 7, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Large ensembles of points with Coulomb interactions arise in various settings of condensed matter physics, classical and quantum mechanics, statistical mechanics, random matrices and even approximation theory, and they give rise to a variety of questions pertaining to analysis, Partial Differential Equations and probability. We will first review these motivations, then present the ”meanfield” derivation of effective models and equations describing the system at the macroscopic scale. We then explain how to analyze the next order behavior, giving information on the configurations at the microscopic level and connecting with crystallization questions, and finish with the description of the effect of temperature.
Talk will be followed by Tea in the Math Common Room – Science Center, 4th Floor
 8  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: A 6year journey: from gravitational anomaly to a unified theory of generalized symmetry
Speaker: XiaoGang Wen – MIT 10:00 AM11:30 AM September 8, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topologicalorder correspondence. I will also discuss some applications of emergent generalized symmetry.
This seminar will be in person and virtual. Password: cmsa For more information, please see:
 HARVARDMIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: The totally nonnegative tropical flag variety
Speaker: Jon Boretsky – Harvard University 3:00 PM4:00 PM September 8, 2023
The flag variety of rank r=(r_1,…,r_k) has points corresponding to collections of subspaces (V_1,…, V_k) with V_i of dimension r_i such that V_i is contained in V_{i+1}. It can be embedded into a multiprojective space, where it is cut out by the incidence Plücker relations. We explore two extensions of this variety: First, we study the nonnegative flag variety, which corresponds to a subset of the flag variety consisting of flags that can be represented by totally positive matrices. Second, we study the tropicalization of the flag variety and, more specifically, its nonnegative part. In both cases, we provide equivalent descriptions of these spaces for flag varieties of rank r=(a,a+1,…,b), where r consists of consecutive integers. We also explore descriptions of the nonnegative tropical flag variety in terms of polytopal subdivisions. Finally, based on explicit computations, we highlight a number of possible fan structures on the totally nonnegative tropical flag variety. This talk is based on joint work with Chris Eur and Lauren Williams. =============================== For more info, see https://math.mit.edu/combin/
 9 
10  11  COLLOQUIUMS: Special Colloquium: Quantitative homogenization, renormalization and anomalous diffusion
Speaker: Scott Armstrong – NYU Courant Institute 3:00 PM4:30 PM September 11, 2023 1 Oxford Street, Cambridge, MA 02138 USA
I will begin the talk with an overview of the topic of quantitative homogenization for elliptic and parabolic equations. Homogenization refers to the procedure of replacing a very “noisy” equation– one with rapidly oscillating coefficients– with a nicer, “effective” equation in a largescale limit. There is a very abstract theory of (qualitative) homogenization, which is classical. We will discuss the more concrete theory of quantitative homogenization, which has been developed recently. A central role in the story concerns certain “coarsegraining” arguments, which can be seen as constituting a rigorous renormalization grouptype approach, formulated in the language of analysis. These methods have surprising applications in mathematical physics and probability, which are still emerging. In the second part of the talk, I will discuss one such application (in a recent joint work with V. Vicol) to turbulence theory: namely, a proof of anomalous diffusion for an advectiondiffusion equation.
Talk will be followed by Tea in the Math Common Room – Science Center, 4th Floor
 12  CMSA EVENT: CMSA General Relativity Seminar: Pole skipping, quasinormal modes, shockwaves and their connection to chaos
Speaker: Diandian Wang – Harvard University 11:00 AM12:00 PM September 12, 2023 20 Garden Street, Cambridge, MA 02138 A chaotic quantum system can be studied using the outoftimeorder correlator (OTOC). I will tell you about pole skipping — a recently discovered feature of the retarded Green’s function — that seems to also know things: things like the Lyapunov exponent and the butterfly velocity, which are important quantifiers of the OTOC. Then I will talk about a systematic way of deriving poleskipping conditions for general holographic CFTs dual to classical bulk theories and how to use this framework to derive a few interesting statements including: (1) theories with higher spins generally violate the chaos bound; (2) the butterfly velocity calculated using pole skipping agrees with that calculated using shockwaves for arbitrary higherderivative gravity coupled to ordinary matter; (3) shockwaves are related to a special type of quasinormal modes. As we will see, the techniques are entirely classically gravitational, which I will go through with a certain level of details.
Zoom Link: https://harvard.zoom.us/j/99317037992 Password: cmsa  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Enumerative geometry, wallcrossing and Virasoro constraints
Speaker: Miguel Moreira – MIT 3:00 PM4:00 PM September 12, 2023
Given a moduli space of either sheaves on a smooth projective variety or a moduli space of representations of a quiver, there are several invariants that we can extract. One of the ways to get numbers out of a moduli space is to integrate (possibly against a virtual fundamental class) certain tautological classes. Such numbers often have interesting structures behind, and I will talk about two: how they change when one changes a stability condition (wallcrossing formulas) and some universal and explicit linear relations that those invariants always seem to satisfy (Virasoro constraints). Both of these phenomena are related to a vertex algebra found by D. Joyce. For simplicity I will mostly focus on the case of representations of a quiver. The talk is based on joint work with A. Bojko and W. Lim.  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Homotopy classes of loops of Clifford unitaries
Speaker: Roman Geiko – UCLA 4:00 PM5:00 PM September 12, 2023 20 Garden Street, Cambridge, MA 02138 We study Clifford localitypreserving unitaries and stabilizer Hamiltonians by means of Hermitian Ktheory. We demonstrate how the notion of algebraic homotopy of modules over Laurent polynomial rings translates into the connectedness of two shortrange entangled stabilizer Hamiltonians by a shallow Clifford circuit. We apply this observation to a classification of homotopy classes of loops of Clifford unitaries. The talk is based on a work in collaboration with Yichen Hu https://arxiv.org/abs/2306.09903.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/97514733653?pwd=Q05XN3oxSnYvaXlnS0dsRnVyMXZMUT09 Password: 353114
 13  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Phase transitions out of quantum Hall states in moire TMD bilayers
Speaker: Xueyang Song – MIT 10:30 AM11:30 AM September 13, 2023 20 Garden Street, Cambridge, MA 02138 Motivated by the recent experimental breakthroughs in observing Fractional Quantum Anomalous Hall (FQAH) states in moir\’e Transition Metal Dichalcogenide (TMD) bilayers, we propose and study various unconventional phase transitions between quantum Hall phases and Fermi liquids or charge ordered phases upon tuning the bandwidth. At filling 2/3, we describe a direct transition between the FQAH state and a Charge Density Wave (CDW) insulator. The critical theory resembles that of the familiar deconfined quantum critical point (DQCP) but with an additional ChernSimons term. At filling 1/2, we study the possibility of a continuous transition between the composite Fermi liquid (CFL) and the Fermi liquid (FL) building on and refining previous work by Barkeshli and McGreevy. Crucially we show that translation symmetry alone is enough to enable a second order CFLFL transition. We argue that there must be critical CDW fluctuations though neither phase has long range CDW order. A striking signature is a universal jump of resistivities at the critical point. With disorder, we argue that the CDW order gets pinned and the CFLFL evolution happens through an intermediate electrically insulating phase with mobile neutral fermions. A clean analog of this insulating phase with long range CDW order and a neutral fermi surface can potentially also exist. We also present a critical theory for the CFL to FL transition at filling 3/4. Our work opens up a new avenue to realize deconfined criticality and fractionalized phases beyond familiar Landau level physics in the moire Chern band system.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/97514733653?pwd=Q05XN3oxSnYvaXlnS0dsRnVyMXZMUT09 Password: 353114  CMSA EVENT: CMSA Quantum Matter in Mathematics and Physics Seminar: Anomalies of NonInvertible Symmetries
Speaker: Clay Córdova – University of Chicago 4:30 PM6:00 PM September 13, 2023 1 Oxford Street, Cambridge, MA 02138 USA
This seminar will be in person and virtual. Password: cmsa For more information, please see:
 14  CMSA EVENT: CMSA Colloquium: An invitation to strongfield scattering
Speaker: Tim Adamo – University of Edinburgh 12:30 PM1:30 PM September 14, 2023 20 Garden Street, Cambridge, MA 02138 Scattering amplitudes in strong background fields provide an arena where perturbative and nonperturbative physics meet, with important applications ranging from laser physics to black holes, but their study is hampered by the cumbersome nature of QFT in the background field formalism. In this talk, I will try to convince you that strongfield scattering amplitudes contain a wealth of physical information which cannot be obtained with standard perturbative techniques, ranging from allorder classical observables to constraints on exact solutions. Furthermore, I will discuss how amplitudes in certain chiral strong fields can be obtained to allmultiplicity twistor and string methods.
 CMSA EVENT: CMSA Active Matter Seminar: Frustrationfree states of cell fate networks: the case of the epithelialmesenchymal transition
Speaker: Herbert Levine – Northeastern University 1:00 PM2:00 PM September 14, 2023 20 Garden Street, Cambridge, MA 02138
Cell fate decisions are made by allowing external signals to govern the steadystate pattern adopted by networks of interacting regulatory factors governing transcription and translation. One of these decisions, of importance for both developmental processes and for cancer metastasis, is the epithelialmesenchymal transition (EMT). In this talk, we will argue that these biological networks have highly nongeneric interaction structures such that they allow for phenotypic states with very low frustration, i.e. where most interactions are satisfied. This property has important consequences for the allowed dynamics of these systems.
This seminar will be held in person and on Zoom. For more information on how to join, please see: https://harvard.zoom.us/j/96657833341
 15  GAUGETOPOLOGYSYMPLECTIC SEMINAR: Gauge Theory and Topology Seminar: Towards isomorphisms among Floer homologies
Speaker: Fan Ye – Harvard University 3:30 PM4:30 PM September 15, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Since Floer’s work in 1988, various Floer homologies have been constructed for closed 3manifolds, knots, and sutured manifolds. In 2008, KronheimerMrowka proposed a conjecture about isomorphisms among Floer homologies. In this talk, I will introduce an approach to proving the isomorphisms and mention some partial results, based on combinatorial version of Floer homology. This work is joint with Baldwin, Li, and Sivek.
 16 
17  18  19  CMSA EVENT: CMSA General Relativity Seminar: Quantization of causal diamonds in 2+1 dimensional gravity
Speaker: Rodrigo Silva – University of Maryland 11:00 AM12:00 PM September 19, 2023
We develop the reduced phase space quantization of causal diamonds in $2+1$ dimensional gravity with a nonpositive cosmological constant. The system is defined as the domain of dependence of a spacelike topological disk with a fixed boundary metric. By solving the constraints in a constantmeancurvature time gauge and removing all the spatial gauge redundancy, we find that the phase space is the cotangent bundle of $Diff^+(S^1)/PSL(2, \mathbb{R})$, i.e., the group of orientationpreserving diffeomorphisms of the circle modulo the projective special linear subgroup. Classically, the states correspond to causal diamonds embedded in $AdS_3$ (or $Mink_3$ if $\Lambda = 0$), with a fixed corner length, that has the topological disk as a Cauchy surface. Because this phase space does not admit a global system of coordinates, a generalization of the standard canonical (coordinate) quantization is required — in particular, since the configuration space is a homogeneous space for a Lie group, we apply Isham’s grouptheoretic quantization scheme. The Hilbert space of the associated quantum theory carries an irreducible unitary representation of the $BMS_3$ group and can be realized by wavefunctions on a coadjoint orbit of Virasoro with labels in irreducible unitary representations of the corresponding little group. A surprising result is that the twist of the diamond boundary loop is quantized in terms of the ratio of the Planck length to the corner length.
Zoom: https://harvard.zoom.us/j/7855806609 Password: cmsa  HARVARDMIT ALGEBRAIC GEOMETRY SEMINAR: Harvard–MIT Algebraic Geometry Seminar: Cycling in Cambridge
Speaker: Elden Elmanto – University of Toronto 3:00 PM4:00 PM September 19, 2023
I spent most of my time here cycling (or is it biking?) and thinking about algebraic cycles from a homotopical viewpoint. I will speak about the latter. In joint work with Matthew Morrow, we developed a theory of motivic cohomology of schemes beyond the case of smooth schemes over a field. I will explain the cycletheoretic aspects of this construction, focusing on the case of surfaces, revisiting older results of Krishna and Srinivas.
 20  CMSA EVENT: CMSA Topological Quantum Matter Seminar: Exact Results in Flat Band Hubbard Models
Speaker: Jonah HerzogArbeitman – Princeton University 10:30 AM11:30 AM September 20, 2023 20 Garden Street, Cambridge, MA 02138 Flat bands, like those in the kagome lattice or twisted bilayer graphene, are a natural setting for studying strongly coupled physics since the interaction strength is the only energy scale in the problem. They can exhibit unconventional behavior in the multiorbital case: the meanfield theory of flat band attractive Hubbard models shows the possibility of superconductivity even though the Fermi velocity of the bands is strictly zero. However, it is not necessary to resort to this approximation. We demonstrate that the groundstates and lowenergy excitations of a large class of attractive Hubbard models are exactly solvable, offering a rare, microscopic view of their physics. The solution reveals the importance of quantum geometry in escaping (some of) BCS phenomenology within a tractable and nontrivial strong coupling theory.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/97514733653?pwd=Q05XN3oxSnYvaXlnS0dsRnVyMXZMUT09 Password: 353114  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 20, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09  NUMBER THEORY SEMINAR: Number Theory Seminar: Harris–Venkatesh plus Stark
Speaker: Robin Zhang – MIT 3:00 PM4:00 PM September 20, 2023 1 Oxford Street, Cambridge, MA 02138 USA The class number formula describes the behavior of the Dedekind zeta function at $s=0$ and $s=1$. The Stark conjecture extends the class number formula, describing the behavior of Artin $L$functions and $p$adic $L$functions at $s=0$ and $s=1$ in terms of units. The Harris–Venkatesh conjecture describes the residue of Stark units modulo $p$, giving a modular analogue to the Stark and Gross conjectures while also serving as the first verifiable part of the broader conjectures of Venkatesh, Prasanna, and Galatius. In this talk, I will draw an introductory picture, formulate a unified conjecture combining Harris–Venkatesh and Stark for weight one modular forms, and describe the proof of this in the imaginary dihedral case.  CMSA EVENT: CMSA Probability Seminar: Solving spin systems, the Babylonian way
Speaker: Nicola Kistler – Johann Wolfgang GoetheUniversität Frankfurt am Main 3:30 PM4:30 PM September 20, 2023 20 Garden Street, Cambridge, MA 02138
The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We are still far from a clear understanding of the issues, but quite astonishingly, evidence is mounting that Parisi’s ultrametricity assumption, the onset of scales and the universal hierarchical selforganisation of random systems in the infinite volume limit, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.  HARVARDMIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: An SL(4) web basis from hourglass plabic graphs
Speaker: Christian Gaetz – Cornell 4:15 PM5:15 PM September 20, 2023
The SL(3) web basis is a special basis of certain spaces of tensor invariants developed in the late 90’s by Khovanov and Kuperberg as a tool for computing quantum link invariants. Since then this basis has found connections and applications to cluster algebras, canonical bases, dimer models, quantum topology, and tableau combinatorics. A main open problem has remained: how to find a basis replicating the desirable properties of this basis for SL(4) and beyond? I will describe joint work with Oliver Pechenik, Stephan Pfannerer, Jessica Striker, and Josh Swanson in which we construct such a basis for SL(4). Modified versions of plabic graphs and the sixvertex model and new tableau combinatorics will appear along the way. =============================== For more info, see https://math.mit.edu/combin/  OPEN NEIGHBORHOOD SEMINAR: Open Neighborhood Seminar: A moduli space problem in condensed matter physics
Speaker: Dan Freed – Harvard University 4:30 PM5:30 PM September 20, 2023 1 Oxford Street, Cambridge, MA 02138 USA
This talk is an elementary account of what is at first a surprising application of stable homotopy theory to theoretical physics. No specialized background is required; the storyline is the focus, not technical details. The main result is a classification of invertible gapped phases in quantum mechanical systems. We will take a journey to get there, along the way meeting moduli problems in geometry and topological field theory. This is joint work with Mike Hopkins. =============================== https://people.math.harvard.edu/~gammage/ons/
 21  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 21, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09  SEMINARS: Thursday Seminar: Introduction to topological quantum field theories
Speaker: Michael Hopkins – Harvard University 3:30 PM5:30 PM September 21, 2023 1 Oxford Street, Cambridge, MA 02138 USA
The theme of the Thursday Seminar this term is “topological aspects of quantum field theory.” The first lecture will be a brief overview, followed by an introduction to topological quantum field theories.  SEMINARS: Algebraic Dynamics Seminar: The abc, abcd, abcde… conjectures and their implications on uniform boundedness
Speaker: Robin Zhang – MIT 4:00 PM6:00 PM September 21, 2023
We start with an introduction to Szpiro’s conjecture and its equivalent formulation, the abc conjecture. Szpiro’s goal in the 1980s was to prove the Mordell conjecture (effectively too!); it was soon observed that the implications of this conjecture and its alternate versions also include landmarks such as Fermat’s Last Theorem, Baker’s theorem, Roth’s theorem, and the nonexistence of Siegel zeroes for certain Dirichlet Lfunctions. We will then highlight recent work by Nicole Looper on new implications in arithmetic dynamics, in particular that the abcd conjecture implies uniform boundedness for preperiodic points of polynomials as well as a weak dynamical Lang’s conjecture for points of small height. http://people.math.harvard.edu/~demarco/AlgebraicDynamics/
 22  CMSA EVENT: CMSA Quantum Matter in Mathematic and Physics Seminar: Floquet codes, automorphisms, and quantum computation
Speaker: Margarita Davydova – MIT 10:00 AM11:30 AM September 22, 2023 20 Garden Street, Cambridge, MA 02138 In this talk, I will introduce a new kind of measurementbased quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of lowweight measurements which simultaneously encode logical information and enable error correction. We introduce a new class of quantum errorcorrecting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes. As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of timelike domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model. This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes. The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two and, rarely threebody measurements. Using adaptive twobody measurements, we can achieve a nonClifford gate in 3+1d, making the first step towards universal quantum computation in this model. The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/977347126 Password: cmsa  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 22, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09  HARVARDMIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Pair constructions for hypergraph Ramsey numbers
Speaker: Xiaoyu He – Princeton University 3:00 PM4:00 PM September 22, 2023
The Ramsey number r_k(G, H) of two kuniform hypergraphs G and H is the smallest n such that any edgecoloring of the complete kuniform hypergraph on n vertices contains either a red copy of G or a blue copy of H. Hypergraph Ramsey theory is concerned with the growth rates of such Ramsey numbers, particularly when one or both of {G, H} is a clique of size tending to infinity. Classical arguments of ErdősRado and ErdősHajnal reduce most major problems in this area from all higher uniformities to uniformity k=3, but fail to bridge the gap from the graph case k=2 to the hypergraph case k=3. In this talk, we survey the known approaches for lifting Ramsey graphs to 3uniform hypergraphs, most famously the steppingup construction of ErdősHajnal. We collect these constructions under the umbrella term “pair constructions” and present new variations proving new lower bounds. In particular, we describe an explicit family of 3uniform hypergraphs H (including links of odd cycles and tight cycles of length not divisible by 3) which satisfy r_3(H, K_n) > 2^{c n log n}. We also prove the existence of a linear 3uniform hypergraph H for which r_3(H, K_n) grows superpolynomially. Based on joint work with David Conlon, Benjamin Gunby, Jacob Fox, Dhruv Mubayi, Andrew Suk, and Jacques Verstraete. =============================== For more info, see https://math.mit.edu/combin/  HARVARDMIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Coefficientwise Hankeltotal positivity
Speaker: Alan Sokal – University College London 3:00 PM4:00 PM September 22, 2023
A matrix M of real numbers is called totally positiveif every minor of $M$ is nonnegative. Gantmakher and Krein showedin 1937 that a Hankel matrix $H = (a_{i+j})_{i,j \ge 0}$of real numbers is totally positive if and only if the underlyingsequence $(a_n)_{n \ge 0}$ is a Stieltjes moment sequence,i.e.\ the moments of a positive measure on $[0,\infty)$.Here I will introduce a generalization: a matrix $M$ of polynomials(in some set of indeterminates) will be called{\em coefficientwise totally positive}\/ if every minor of $M$is a polynomial with nonnegative coefficients. And a sequence$(a_n)_{n \ge 0}$ of polynomials will be called{\em coefficientwise Hankeltotally positive}\/ if the Hankel matrix$H = (a_{i+j})_{i,j \ge 0}$ associated to $(a_n)$ is coefficientwisetotally positive.It turns out that many sequences of polynomials arising naturallyin enumerative combinatorics are (empirically) coefficientwiseHankeltotally positive. I will discuss some methods for proving this.But these proofs fall far short of what appears to be true. =============================== For more info, see https://math.mit.edu/combin/
 23  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 23, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09

24  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 24, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09
 25  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 25, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09  CMSA EVENT: CMSA Colloquium: Predicting noncontinuous functions
Speaker: Sean Cox – Virginia Commonwealth University 4:30 PM5:30 PM September 25, 2023 20 Garden Street, Cambridge, MA 02138 One of the strangest consequences of the Axiom of Choice is the following HardinTaylor 2008 result: there is a “predictor” such that for every function $f$ from the reals to the reals—even nowhere continuous $f$—the predictor applied to $f \restriction (\infty,t)$ correctly predicts $f(t)$ for *almost every* $t \in R$. They asked how robust such a predictor could be, with respect to distortions in the time (input) axis; more precisely, for which subgroups $H$ of Homeo^+(R) do there exist $H$invariant predictors? BajpaiVelleman proved an affirmative answer when H=Affine^+(R), and a negative answer when H is (the subgroup generated by) C^\infty(R). They asked about the intermediate region; in particular, do there exist analyticinvariant predictors? We have partially answered that question: assuming the Continuum Hypothesis (CH), the answer is “no”. Regarding other subgroups of Homeo^+(R), we have affirmative answers that rely solely on topological grouptheoretic properties of the subgroup. But these properties are very restrictive; e.g., all known positive examples are metabelian. So there remain many open questions. This is joint work with Aldi, Buffkin, Cline, Cody, Elpers, and Lee.
 26  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 26, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09
 27  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: Transformers for maths, and maths for transformers
Speaker: François Charton – Meta AI 2:00 PM3:00 PM September 27, 2023 20 Garden Street, Cambridge, MA 02138
Transformers can be trained to solve problems of mathematics. I present two recent applications, in mathematics and physics: predicting integer sequences, and discovering the properties of scattering amplitudes in a close relative of Quantum ChromoDynamics. Problems of mathematics can also help understand transformers. Using two examples from linear algebra and integer arithmetic, I show that model predictions can be explained, that trained models do not confabulate, and that carefully choosing the training distributions can help achieve better, and more robust, performance.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09  CMSA EVENT: CMSA New Technologies in Mathematics Seminar: The TinyStories Dataset: How Small Can Language Models Be And Still Speak Coherent English?
Speaker: Ronan Eldan – Microsoft Research 2:00 PM3:00 PM September 27, 2023September 27, 2023 20 Garden Street, Cambridge, MA 02138
While generative language models exhibit powerful capabilities at large scale, when either the model or the number of training steps is too small, they struggle to produce coherent and fluent text: Existing models whose size is below a few billion parameters often do not generate coherent text beyond a few sentences. Hypothesizing that one of the main reasons for the strong reliance on size is the vast breadth and abundance of patterns in the datasets used to train those models, this motivates the following question: Can we design a dataset that preserves the essential elements of natural language, such as grammar, vocabulary, facts, and reasoning, but that is much smaller and more refined in terms of its breadth and diversity? In this talk, we introduce TinyStories, a synthetic dataset of short stories that only contain words that 3 to 4yearolds typically understand, generated by GPT3.5/4. We show that TinyStories can be used to train and analyze language models that are much smaller than the stateoftheart models (below 10 million parameters), or have much simpler architectures (with only one transformer block), yet still produce fluent and consistent stories with several paragraphs that are diverse and have almost perfect grammar, and demonstrate certain reasoning capabilities. We also show that the trained models are substantially more interpretable than larger ones, as we can visualize and analyze the attention and activation patterns of the models, and show how they relate to the generation process and the story content. We hope that TinyStories can facilitate the development, analysis and research of language models, especially for lowresource or specialized domains, and shed light on the emergence of language capabilities in LMs.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/95706757940?pwd=dHhMeXBtd1BhN0RuTWNQR0xEVzJkdz09  NUMBER THEORY SEMINAR: Number Theory Seminar: TBA
Speaker: Tom Weston – UMass Amherst 3:00 PM4:00 PM September 27, 2023 1 Oxford Street, Cambridge, MA 02138 USA  HARVARDMIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Some enumerative properties of parking functions and labelled forests
Speaker: Mei Yin – University of Denver 4:15 PM5:15 PM September 27, 2023
A parking function is a sequence (a_1,…,a_n) of positive integers such that if b_1<=…<=b_n is the increasing rearrangement of a_1,…,a_n, then b_i<=i for 1<=i<=n. Parking functions of length n are in bijection with labelled forests on the vertex set [n]={1,2,…,n} (or rooted trees on [n]_0={0,1,…,n} with root 0). We obtain some new results on the enumeration of parking functions and labelled forests, concentrating in particular on the joint distribution of several sets of statistics on parking functions. The distribution of most of these individual statistics is known, but the joint distributions are new. Extensions of our techniques are discussed. Joint work with Richard Stanley and with Stephan Wagner. =============================== For more info, see https://math.mit.edu/combin/
 28  CMSA EVENT: CMSA Active Matter Seminar: Frustrationfree states of cell fate networks: Strongly driven mixtures and membranes: Out of equilibrium surprises
Speaker: Max Lavrentovich – Worcester State University 1:00 PM2:00 PM September 28, 2023 20 Garden Street, Cambridge, MA 02138
The more prosaic cousin of active matter, driven inactive matter, is still full of unexpected phenomena. I will discuss two projects involving two seemingly mundane systems, a phaseseparating colloidal mixture and a lipid membrane, which demonstrate counterintuitive properties when driven out of equilibrium. We will see that the phase separating mixture, when driven by a uniform force, develops (in simulations) an intriguing pattern with a characteristic length scale set by the magnitude of the drive. We will look at some theoretical approaches to understanding the pattern formation and possible experimental realizations. The membrane, when driven by an oscillatory electric field, develops (in experiments) a longlived metastable state with a decreased capacitance and increased dissipation. This state may have implications for neuronal processing and memory formation.
This seminar will be held in person and on Zoom. For more information on how to join, please see: https://harvard.zoom.us/j/96657833341  COLLOQUIUMS: Special Colloquium: Interface Fluctuations in Random Surface Models
Speaker: Amol Aggarwal – Columbia University 3:00 PM4:30 PM September 28, 2023 1 Oxford Street, Cambridge, MA 02138 USA
Random surfaces are central paradigms in equilibrium statistical mechanics. As these surfaces become larger, their statistical behaviors become strongly dependent on how their boundaries are pinned down. This can lead to phase transitions, such as facet edges separating a flat region of the surface from the places where it curves. How do these surfaces look and fluctuate near such interfaces? The purpose of this talk is to explain some of these aspects, and to touch on some of the diverse mathematical concepts that go into its analysis.
Talk will be followed by Tea in the Math Common Room – Science Center, 4th Floor
 29  CMSA EVENT: CMSA Special Seminar: Topological modular forms and heretoric string theory
Speaker: Mayuko Yamashita – Kyoto University 2:00 PM3:00 PM September 29, 2023 20 Garden Street, Cambridge, MA 02138 In this talk I will explain my works with Y. Tachikawa to study anomaly in heterotic string theory via homotopy theory, especially the theory of Topological Modular Forms (TMF). TMF is an Einfinity ring spectrum which is conjectured by StolzTeichner to classify twodimensional supersymmetric quantum field theories in physics. In the previous work (https://arxiv.org/abs/2108.13542), we proved the vanishing of anomalies in heterotic string theory mathematically by using TMF. Furthermore, we have a recent update (https://arxiv.org/abs/2305.06196) on the previous work. Because of the vanishing result, we can consider a secondary transformation of spectra, which is shown to coincide with the Anderson selfduality morphism of TMF. This allows us to detect subtle torsion phenomena in TMF by differentialgeometric ways, and leads us to new conjectures on the relation between VOAs and TMF.
This seminar will be held in person and on Zoom: https://harvard.zoom.us/j/977347126 Password: cmsa  HARVARDMIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Filtrations of tope spaces of oriented matroids
Speaker: Chi Ho Yuen – Oslo 3:00 PM4:00 PM September 29, 2023
Oriented matroids are matroids with extra sign data, and they are useful in the tropical study of real algebraic geometry. In order to study the topology of real algebraic hypersurfaces constructed from patchworking, Renaudineau and Shaw introduced an algebraically defined filtration of the tope space of an oriented matroid based on Quillen filtration. We will prove the equality between their filtration (together with the induced maps), the topologically defined Kalinin filtration, and the combinatorially defined VarchenkoGelfand dual degree filtration over Z/2Z. We will also explain how the dual degree filtration can serve as a Zcoefficient version of the other two in this setting. This is joint work with Kris Shaw. =============================== For more info, see https://math.mit.edu/combin/
 30 