CMSA

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

All CMSA and Math affiliates are invited.

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

Speaker: Nikolaos Athanasiou

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

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

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

Speaker: Melody Chan, Brown

Title: Moduli spaces of graphs

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

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

Speaker: Shenshen Wang, UCLA

Title: Limit and potential of adaptive immunity

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

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

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

Speaker: Samir Mathur (Ohio State)

Title: The story of the information paradox

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

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

Speaker: Shai Chester

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

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

Title: The Gregory-Laflamme instability of black strings revisited

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

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

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

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

Non-invertible Symmetries in Nature
2022-09-13 09:30 - 11:00 | Massachusetts
Quantum Matter in Mathematics and Physics

Speaker: Yichul Cho (SUNY Stony Brook)
Title: Non-invertible Symmetries in Nature
Abstract: In this talk, I will discuss non-invertible symmetries in
familiar 3+1d quantum field theories describing our Nature. In
massless QED, the classical U(1) axial symmetry is not completely
broken by the ABJ anomaly. Instead, it turns into a discrete,
non-invertible symmetry. The non-invertible symmetry operator is
obtained by dressing the naïve U(1) axial symmetry operator with a
fractional quantum Hall state. We also find a similar non-invertible
symmetry in the massless limit of QCD, which provides an alternative
explanation for the neutral pion decay. In the latter part of the
talk, I will discuss non-invertible time-reversal symmetries in 3+1d
gauge theories. In particular, I will show that in free Maxwell
theory, there exists a non-invertible time-reversal symmetry at every
rational value of the theta angle.
Based on https://arxiv.org/abs/2205.05086 and https://arxiv.org/abs/2208.04331.

Duality in Einstein’s Gravity
2022-09-09 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Title: Duality in Einstein’s Gravity
Abstract: Electric-Magnetic duality has been a key feature behind our understanding of Quantum Field Theory for over a century. In this talk I will describe a similar property in Einstein’s gravity. The gravitational duality reveals, in turn, a wide range of new IR phenomena, including aspects of the double copy for scattering amplitudes, asymptotic symmetries and more.

The second law of black hole mechanics in effective field theory
2022-09-08 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Professor Harvey Reall (University of Cambridge)
Title: The second law of black hole mechanics in effective field theory
Abstract: I shall discuss the second law of black hole mechanics in gravitational theories with higher derivative terms in the action. Wall has described a method for defining an entropy that satisfies the second law to linear order in perturbations around a stationary black hole. I shall explain how this can be extended to define an entropy that satisfies the second law to quadratic order in perturbations, provided that one treats the higher derivative terms in the sense of effective field theory. This talk is based on work with Stefan Hollands and Aron Kovacs.
Video

Gifts from anomalies: new results on quantum critical transport in non- Fermi liquids
2022-09-07 09:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Zhengyan Darius Shi (MIT)

Title: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
Abstract: Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result due to Kim et al. is incorrect for inversion-odd order parameters.

State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk
2022-09-06 13:00 - 14:00 | Massachusetts
Speaker: Josef Käs, Leipzig University
Title: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk
Abstract: Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.
Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.
We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.
Video (Youtube)

Big Data Conference 2022
2022-08-26 09:00 - 13:00 | Virtual
On August 26, 2022 the CMSA hosted our eighth 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.
The 2022 Big Data Conference took place virtually on Zoom.
Organizers:

Scott Duke Kominers, MBA Class of 1960 Associate Professor, Harvard Business
Horng-Tzer Yau, Professor of Mathematics, Harvard University
Sergiy Verstyuk, CMSA, Harvard University

Speakers:

Xiaohong Chen, Yale
Miles Cranmer, Princeton
Jessica Jeffers, University of Chicago
Dan Roberts, MIT

Schedule

9:00 am
Conference Organizers
Introduction and Welcome

9:10 am – 9:55 am
Xiaohong Chen
Title: On ANN optimal estimation and inference for policy functionals of nonparametric conditional moment restrictions
Abstract: Many causal/policy parameters of interest are expectation functionals of unknown infinite-dimensional structural functions identified via conditional moment restrictions. Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional covariates more effectively than linear sieves. In this talk we present ANN optimal estimation and inference on policy functionals, such as average elasticities or value functions, of unknown structural functions of endogenous covariates. We provide ANN efficient estimation and optimal t based confidence interval for regular policy functionals such as average derivatives in nonparametric instrumental variables regressions. We also present ANN quasi likelihood ratio based inference for possibly irregular policy functionals of general nonparametric conditional moment restrictions (such as quantile instrumental variables models or Bellman equations) for time series data. We conduct intensive Monte Carlo studies to investigate computational issues with ANN based optimal estimation and inference in economic structural models with endogeneity. For economic data sets that do not have very high signal to noise ratios, there are current gaps between theoretical advantage of ANN approximation theory vs inferential performance in finite samples.
Some of the results are applied to efficient estimation and optimal inference for average price elasticity in consumer demand and BLP type demand.
The talk is based on two co-authored papers:
(1) Efficient Estimation of Average Derivatives in NPIV Models: Simulation Comparisons of Neural Network Estimators
(Authors: Jiafeng Chen, Xiaohong Chen and Elie Tamer)
https://arxiv.org/abs/2110.06763
(2) Neural network Inference on Nonparametric conditional moment restrictions with weakly dependent data
(Authors: Xiaohong Chen, Yuan Liao and Weichen Wang).
View/Download Lecture Slides (pdf)

10:00 am – 10:45 am
Jessica Jeffers
Title: Labor Reactions to Credit Deterioration: Evidence from LinkedIn Activity
Abstract: We analyze worker reactions to their firms’ credit deterioration. Using weekly networking activity on LinkedIn, we show workers initiate more connections immediately following a negative credit event, even at firms far from bankruptcy. Our results suggest that workers are driven by concerns about both unemployment and future prospects at their firm. Heightened networking activity is associated with contemporaneous and future departures, especially at financially healthy firms. Other negative events like missed earnings and equity downgrades do not trigger similar reactions. Overall, our results indicate that the build-up of connections triggered by credit deterioration represents a source of fragility for firms.

10:50 am – 11:35 am
Miles Cranmer
Title: Interpretable Machine Learning for Physics
Abstract: Would Kepler have discovered his laws if machine learning had been around in 1609? Or would he have been satisfied with the accuracy of some black box regression model, leaving Newton without the inspiration to discover the law of gravitation? In this talk I will explore the compatibility of industry-oriented machine learning algorithms with discovery in the natural sciences. I will describe recent approaches developed with collaborators for addressing this, based on a strategy of “translating” neural networks into symbolic models via evolutionary algorithms. I will discuss the inner workings of the open-source symbolic regression library PySR (github.com/MilesCranmer/PySR), which forms a central part of this interpretable learning toolkit. Finally, I will present examples of how these methods have been used in the past two years in scientific discovery, and outline some current efforts.
View/Download Lecture Slides (pdf)

11:40 am – 12:25 pm
Dan Roberts
Title: A Statistical Model of Neural Scaling Laws
Abstract: Large language models of a huge number of parameters and trained on near internet-sized number of tokens have been empirically shown to obey “neural scaling laws” for which their performance behaves predictably as a power law in either parameters or dataset size until bottlenecked by the other resource. To understand this better, we first identify the necessary properties allowing such scaling laws to arise and then propose a statistical model — a joint generative data model and random feature model — that captures this neural scaling phenomenology. By solving this model using tools from random matrix theory, we gain insight into (i) the statistical structure of datasets and tasks that lead to scaling laws (ii) how nonlinear feature maps, i.e the role played by the deep neural network, enable scaling laws when trained on these datasets, and (iii) how such scaling laws can break down, and what their behavior is when they do. A key feature is the manner in which the power laws that occur in the statistics of natural datasets are translated into power law scalings of the test loss, and how the finite extent of such power laws leads to both bottlenecks and breakdowns.
View/Download Lecture Slides (pdf)

12:30 pm
Conference Organizers
Closing Remarks

Information about last year’s conference can be found here.

Scalable Dynamic Graph Algorithms
2022-08-18 10:00 - 10:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Interdisciplinary Science Seminar
Speaker: Quanquan Liu, Northwestern University
Title: Scalable Dynamic Graph Algorithms
Abstract: The field of dynamic graph algorithms seeks to understand and compute statistics on real-world networks that undergo changes with time. Some of these networks could have up to millions of edge insertions and deletions per second. In light of these highly dynamic networks, we propose various scalable and accurate graph algorithms for a variety of problems. In this talk, I will discuss new algorithms for various graph problems in the batch-dynamic model in shared-memory architectures where updates to the graph arrive in multiple batches of one or more updates. I’ll also briefly discuss my work in other dynamic models such as distributed dynamic models where the communication topology of the network also changes with time (ITCS 2022). In these models, I will present efficient algorithms for graph problems including k-core decomposition, low out-degree orientation, matching, triangle counting, and coloring.
Specifically, in the batch-dynamic model where we are given a batch of B updates, I’ll discuss an efficient O(B log^2 n) amortized work and O(log^2 n log log n) depth algorithm that gives a (2+epsilon)-approximation on the k-core decomposition after each batch of updates (SPAA 2022). We also obtain new batch-dynamic algorithms for matching, triangle counting, and coloring using techniques and data structures developed in our k-core decomposition algorithm. In addition to our theoretical results, we implemented and experimentally evaluated our k-core decomposition algorithm on a 30-core machine with two-way hyper-threading on 11 graphs of varying densities and sizes. Our experiments show improvements over state-of-the-art algorithms even on machines with only 4 cores (your standard laptop). I’ll conclude with a discussion of some open questions and potential future work that these lines of research inspire.
Bio: Quanquan C. Liu is a postdoctoral scholar at Northwestern University under the mentorship of Prof. Samir Khuller. She completed her PhD in Computer Science at MIT where she was advised by Prof. Erik Demaine and Prof. Julian Shun. Before that, she obtained her dual bachelor’s degree in computer science and math also at MIT. She has worked on a number of problems in algorithms and the intersection between theory and practice. Her most recent work focuses on scalable dynamic and static graph algorithms as well as differentially private graph algorithms for problems including k-core decomposition, densest subgraphs, subgraph counting, matching, maximal independent set and coloring. She has earned the Best Paper Award at SPAA 2022, a NSF Graduate Research Fellowship, and participated in the 2021 EECS Rising Stars workshop. Outside of research, she is extensively involved in programming outreach as a coach for the USA Computing Olympiad (USACO) and as a trainer for the North America Programming Camp (NAPC).

Transport in large-N critical Fermi surface
2022-08-16 10:00 - 11:30 | Virtual
Speaker: Haoyu Guo (Harvard)
Title: Transport in large-N critical Fermi surface

Abstract: A Fermi surface coupled to a scalar field can be described in a 1/N expansion by choosing the fermion-scalar Yukawa coupling to be random in the N-dimensional flavor space, but invariant under translations. We compute the conductivity of such a theory in two spatial dimensions for a critical scalar. We find a Drude contribution, and show that a previously proposed omega^{-2/3} contribution to the optical conductivity at frequency omega has vanishing co-efficient. We also describe the influence of impurity scattering of the fermions, and find that while the self energy resembles a marginal Fermi liquid, the resistivity behaves like a Fermi liquid. Arxiv references: 2203.04990, 2207.08841

Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning
2022-08-11 09:00 - 10:00 | Hybrid
Interdisciplinary Science Seminar
Speaker: Yue M. Lu, Harvard University
Title: Exploring and Exploiting the Universality Phenomena in High-Dimensional Estimation and Learning
Abstract: Universality is a fascinating high-dimensional phenomenon. It points to the existence of universal laws that govern the macroscopic behavior of wide classes of large and complex systems, despite their differences in microscopic details. The notion of universality originated in statistical mechanics, especially in the study of phase transitions. Similar phenomena have been observed in probability theory, dynamical systems, random matrix theory, and number theory.
In this talk, I will present some recent progresses in rigorously understanding and exploiting the universality phenomena in the context of statistical estimation and learning on high-dimensional data. Examples include spectral methods for high-dimensional projection pursuit, statistical learning based on kernel and random feature models, and approximate message passing algorithms on highly structured, strongly correlated, and even (nearly) deterministic data matrices. Together, they demonstrate the robustness and wide applicability of the universality phenomena.
Bio: Yue M. Lu attended the University of Illinois at Urbana-Champaign, where he received the M.Sc. degree in mathematics and the Ph.D. degree in electrical engineering, both in 2007. He is currently Gordon McKay Professor of Electrical Engineering and of Applied Mathematics at Harvard University. He is also fortunate to have held visiting appointments at Duke University in 2016 and at the École Normale Supérieure (ENS) in 2019. His research interests include the mathematical foundations of statistical signal processing and machine learning in high dimensions.

Recent Advances on Maximum Flows and Minimum-Cost Flows
2022-08-10 09:00 - 10:00 | Virtual
Interdisciplinary Science Seminar

Speaker: Yang P. Liu

Title: Recent Advances on Maximum Flows and Minimum-Cost Flows

Abstract: We survey recent advances on computing flows in graphs, culminating in an almost linear time algorithm for solving minimum-cost flow and several other problems to high accuracy on directed graphs. Along the way, we will discuss intuitions from linear programming, graph theory, and data structures that influence these works, and the resulting natural open problems.
Bio: Yang P. Liu is a final-year graduate student at Stanford University. He is broadly interested in the efficient design of algorithms, particularly flows, convex optimization, and online algorithms. For his work, he has been awarded STOC and ITCS best student papers.

Phase Transitions and Topological Defects in the Early Universe
2022-08-02 09:00 - 2022-08-05 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
On August 2–5, the CMSA hosted a workshop on Phase Transitions and Topological Defects in the Early Universe.
The workshop was held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA and online via Zoom webinar.
The next decade will see a wealth of new cosmological data, which can lead to new insights into fundamental physics. Upcoming facilities (such as LISA) will be able to probe signals of fascinating phenomena in the early universe. These include signals from “Phase Transitions and Topological Defects,” which are ubiquitously given rise to in well-motivated UV models. In-depth studies of such signals requires cross-talks between experts from a wide spectrum of fields.
The workshop aims to provide a platform for efficient exchange of new ideas related to these topics. It will start with an overview of some of the past and future experimental efforts. Next, there will be a substantial number of talks probing different aspects of phenomenology of phase transitions and topological defects in the early universe. It will finally close with discussions on recent formal development in the field.
Scientific Advisory: Julian B. Muñoz, Lisa Randall, Matthew Reece, Tracy Slatyer, Shing-Tung Yau
Organizers:
Harvard: Nick DePorzio, Katie Fraser, Sam Homiller, Rashmish Mishra, & Aditya Parikh
MIT: Pouya Asadi, Marianne Moore, & Yitian Sun
Schedule/Format
There will be 20+ 10 minute talks, ample discussion time, and lightning chalkboard talks.
Speakers:

Nancy Aggarwal (Northwestern)
Jae Hyeok Chang (UMD – JHU)
Yanou Cui (UC Riverside)
David Dunsky (UC Berkeley)
Isabel Garcia-Garcia (KITP – UCSB)
Oliver Gould (Nottingham)
Yann Gouttenoire (Tel Aviv)
Eleanor Hall (UC Berkeley)
Sungwoo Hong (Chicago)
Anson Hook (UMD)
Jessica Howard (UC Irvine)
Seth Koren (Chicago)
Mrunal Korwar (Wisconsin)
Soubhik Kumar (UC Berkeley)
Vuk Mandic (Minnesota)
Yuto Minami (Osaka)
Michael Nee (Oxford)
Kai Schmitz (CERN)
Stephen R. Taylor (Vanderbilt)
Ofri Telem (UC Berkeley)
Juven Wang (Harvard)
Yikun Wang (Caltech)

Participants:

Manuel Buen Abad (UMD)
Pouya Asadi (MIT)
Sean Benevedes (MIT)
Sandipan Bhattacherjee (Birla Institute of Technology Mesra Ranchi India)
Xingang Chen (Harvard University)
Nicholas DePorzio (Harvard University)
Peizhi Du (Stony Brook University)
Nicolas Fernandez (University of Illinois Urbana-Champaign)
Joshua Foster (MIT)
Katherine Fraser (Harvard University)
Sarah Geller (MIT)
Aurora Ireland (University of Chicago)
Marius Kongsore (New York University)
Ho Tat Lam (Massachusetts Institute of Technology)
Lingfeng Li (Brown University)
Yingying Li (Fermilab)
Gustavo Marques-Tavares (UMD)
Rashmish Mishra (Harvard University)
Siddharth Mishra-Sharma (MIT/Harvard University)
Toby Opferkuch (UC Berkeley)
Tong Ou (University of Chicago)
Aditya Parikh (Harvard University)
Yitian Sun (MIT)
Juan Sebastian Valbuena-Bermudez (Ludwig Maximilian University of Munich and Max Planck Institute for Physics)
Isaac Wang (Rutgers)
Wei Xue (University of Florida)
Winston Yin (UC Berkeley)
Quratulain Zahoor (The Islamia University of Bahwalpur Punjab (Pakistan)

Schedule
Tuesday, August 2, 2022

9:00–9:20 am
Breakfast

9:20–9:30 am
Rashmish Mishra
Opening Remarks

9:30–10:00 am
Vuk Mandic
Title: Searching for the Stochastic Gravitational Wave Background with LISA
Abstract: The upcoming space-borne gravitational wave detector Laser Interferometer Space Antenna (LISA) will open a window into the milliHertz band of the gravitational wave spectrum. Among the many sources in this band is the stochastic gravitational wave background (SGWB), arising as an incoherent superposition of many uncorrelated gravitational wave sources. The SGWB could be of cosmological origin, carrying unique information about the physical processes that took place within the first minute after the big bang, including possible phase transitions and topological defects. LISA therefore has the potential to illuminate particle physics at very high energy scales that may be inaccessible in laboratories. I will discuss how LISA can be used to search for the SGWB, highlighting a new pipeline developed for this purpose as well as several challenges and limitations that such a search will encounter.

10:00–10:30 am
Nancy Aggarwal
Title: Gravitational waves at frequencies above 10 kHz
Abstract: Gravitational waves (GWs) at frequencies higher than the LIGO band can bring us completely new information about the universe. Besides being the most-interesting frequency region for looking at cosmological phenomena, they can also convey signatures of ultralight bosons through blackhole superradiance and light primordial blackholes (PBHs). I will introduce a new global initiative to study GW sources and detectors at ultra-high-frequencies (MHz-GHz), as well as a new experiment at Northwestern University to look for GWs in the frequency band of 10 kHz to 300 kHz using levitated optomechanical sensors. I will summarize the design, the current experimental progress, as well as a path forward for future improvements.

10:30–11:00 am
Yuto Minami
Title: New measurements of the cosmic birefringence
Abstract: Polarised light of the cosmic microwave background, the remnant light of the Big Bang, is sensitive to parity-violating physics, cosmic birefringence. In this presentation I report on a new measurement of cosmic birefringence from polarisation data of the European Space Agency (ESA)’s Planck satellite released in 2018. The statistical significance of the measured signal is 2.4 sigma. Recently, we found a signal with 3.3 sigma statistical significance when we use the latest Planck data and consider an effect of polarised foreground emission. If confirmed with higher statistical significance in future, it would have important implications for the elusive nature of dark matter and dark energy.

11:00–1:30 pm
Break

1:30–3:00 pm
Lighting Talks 1
Lingfeng Li
Winston Yin
Marius Kongsore
Nick DePorzio

3:00–3:30 pm
Jae Hyeok Chang
Title: Correlating gravitational wave and gamma-ray signals from primordial black holes
Abstract: Asteroid-mass primordial black holes (PBHs) can explain the observed dark matter abundance while being consistent with the current indirect detection constraints. These PBHs can produce gamma-ray signals from Hawking radiation that are within the sensitivity of future measurements by the AMEGO and e-ASTROGAM experiments. PBHs which give rise to such observable gamma-ray signals have a cosmic origin from large primordial curvature fluctuations. There must then be a companion, stochastic gravitational wave (GW) background produced by the same curvature fluctuations. I will demonstrate that the resulting GW signals will be well within the sensitivity of future detectors such as LISA, DECIGO, BBO, and the Einstein Telescope. The multimessenger signal from the observed gamma-rays and GWs will allow a precise measurement of the primordial curvature perturbation that produces the PBH. I will also argue that the resulting correlation between the two types of observations can provide a smoking-gun signal of PBHs.

3:30–4:00 pm
Anson Hook
(Virtual via Zoom)
Title: Early Universe Cosmology from Stochastic Gravitational Waves
Abstract: The causal tail of stochastic gravitational waves can be used to probe the energy density in free streaming relativistic species as well as measure gstar and beta functions as a function of temperature. In the event of the discovery of loud stochastic gravitational waves, we demonstrate that LISA can measure the free streaming fraction of the universe down to the 10^-3 level, 100 times more sensitive than current constraints. Additionally, it would be sensitive to O(1) deviations of gstar and the QCD beta function from their Standard Model value at temperatures ~ 10^5 GeV. In this case, many motivated models such as split SUSY and other solutions to the Electroweak Hierarchy problem would be tested. Future detectors, such as DECIGO, would be 100 times more sensitive than LISA to these effects and be capable of testing other motivated scenarios such as WIMPs and axions. The amazing prospect of using precision gravitational wave measurements to test such well motivated theories provides a benchmark to aim for when developing a precise understanding of the gravitational wave spectrum both experimentally and theoretically.

Wednesday, August 3, 2022

9:00–9:30 am
Breakfast

9:30–10:00 am
Kai Schmitz
(Virtual via Zoom)
Title: Gravitational waves from metastable cosmic strings
Abstract: Cosmic strings are predicted by many Standard Model extensions involving the cosmological breaking of an Abelian symmetry and represent a potential source of primordial gravitational waves (GWs). In many Grand Unified Theories (GUTs), cosmic strings especially turn out to be metastable, as the nucleation of GUT monopoles along strings after a finite lifetime eventually leads to the collapse of the entire string network. In this talk, I will discuss the theoretical description of such a network and its individual components as well as the consequences for the emitted GW spectrum. Remarkably, the GW signal from metastable strings may well explain the common-spectrum process recently observed in pulsar timing data, while at the same time and in contrast to stable cosmic strings predicting a signal at higher frequencies that is still within the reach of current-generation ground-based interferometers. On their way to design sensitivity, existing GW experiments will thus have a realistic chance to probe particle physics processes at energies close to the GUT scale via the observation of GWs from metastable strings. This talk is based on 2107.04578 in collaboration with Wilfried Buchmüller and Valerie Domcke.

10:00–10:30 am
Oliver Gould
(Virtual via Zoom)
Title: Effective field theory for cosmological phase transitions
Abstract: Phase transitions are driven by thermal loop fluctuations, which modify background fields at leading order. This breaks the loop expansion and leads to large theoretical uncertainties in typical calculations, especially for gravitational wave predictions. I will give an overview of our present understanding of these uncertainties, and of the tools that have been developed to overcome them. Effective field theory has been at the forefront of this development, and I will outline how it can be used to solve a number of decades-long-standing theoretical problems.

10:30–11:00 am
Isabel Garcia-Garcia
Title: The Rocket Science of Expanding Bubbles

11:00–1:30 pm
Break

1:30–3:00 pm
Lightning Talks 2
Sarah Geller
Peizhi Du
Tong Ou
Isaac Wang
Katie Fraser

3:00–3:30 pm
David Dunsky
(Virtual via Zoom)
Title: Gravitational Wave Gastronomy
Abstract: The symmetry breaking of grand unified gauge groups in the early universe often leaves behind relic topological defects such as cosmic strings, domain walls, or monopoles. For some symmetry breaking chains, hybrid defects can form where cosmic strings attach to domain walls or monopoles attach to strings. In general, such hybrid defects are unstable and can leave behind unique gravitational wave fingerprints. In this talk, I will discuss the gravitational wave spectrum from 1) the destruction of a cosmic string network by the nucleation of monopoles which cut up and “eat” the strings, 2) the collapse and decay of a monopole-string network by strings that “eat” the monopoles, 3) the destruction of a domain wall network by the nucleation of string-bounded holes on the wall that expand and “eat” the wall, and 4) the collapse and decay of a string-bounded wall network by walls that “eat” the strings. We call the gravitational wave signals produced from the “eating” of one topological defect by another “gravitational wave gastronomy”. The gravitational wave gastronomy signals considered yield unique spectra that can be used to narrow down the SO(10) symmetry breaking chain to the Standard Model and the scales of symmetry breaking associated with the consumed topological defects.

3:30–4:00 pm
Yanou Cui
(Virtual via Zoom)
Title: Cosmic Archaeology with gravitational waves from (axion) cosmic strings
Abstract: In this talk I will discuss important aspects of cosmology and particle physics that can be probed with GW signals from cosmic strings: probing the pre-BBN primordial dark age and axion physics. Gravitational waves (GWs) originating from the dynamics of a cosmic string network have the ability to probe many otherwise inaccessible properties of the early universe. In particular, I will discuss how the frequency spectrum of a stochastic GW background (SGWB) from a cosmic string network can be used to probe Hubble expansion rate of the early universe prior to Big Bang Nucleosynthesis (BBN), during the “primordial dark age”. Furthermore I will show that in contrast to the standard expectation, cosmic strings formed before inflation could regrow back into the horizon and leave imprints, with GW bursts potentially being the leading signal. In relation to axion physics I will also demonstrate the detection prospect for SGWB from global/axion strings which may provide a new probe for axion-like dark matter models, considering various scenarios of cosmic history.

4:00–4:30 pm
Michael Nee
Title: The Boring Monopole
Abstract: First order phase transitions play an important role in the cosmology of many theories of BSM physics. In this talk I will discuss how a population of magnetic monopoles present in the early universe can seed first order phase transitions, causing them to proceed much more rapidly than in the usual case. The field profiles describing the decay do not have the typically assumed O(3)/O(4) symmetry, thus requiring an extension of the usual decay rate calculation. To numerically determine the saddle point solutions which describe the decay we use a new algorithm based on the mountain pass theorem. Our results show that monopole-catalysed tunnelling can dominate over the homogeneous decay for a wide range of parameters.

Thursday, August 4, 2022

9:00–9:30 am
Breakfast

9:30–10:00 am
Yikun Wang
Title: A New Approach to Electroweak Symmetry Non-Restoration
Abstract: Electroweak symmetry non-restoration up to high temperatures well above the electroweak scale has intriguing implications for (electroweak) baryogenesis and early universe thermal histories. In this talk, I will discuss such a possible fate of the electroweak symmetry in the early universe and a new approach to realize it, via an inert Higgs sector that couples to the Standard Model Higgs as well as an extended scalar singlet sector. Examples of benchmark scenarios that allow for electroweak symmetry non-restoration all the way up to hundreds of TeV temperatures, at the same time featuring suppressed sphaleron washout factors down to the electroweak scale, will be presented. Renormalization group improvements and thermal resummation, necessary to evaluate the effective potential spanning over a broad range of energy scales and temperatures, have been implemented calculating the thermal history. This method for transmitting the Standard Model broken electroweak symmetry to an inert Higgs sector can be scrutinized through Higgs physics phenomenology and electroweak precision measurements at the HL-LHC.

10:00–10:30 am
Soubhik Kumar
Title: Probing primordial fluctuations through stochastic gravitational wave background anisotropies
Abstract: Stochastic gravitational wave backgrounds are expected to be anisotropic. While such anisotropies can be of astrophysical origin, a cosmological component of such anisotropies can carry rich information about primordial perturbations. Focusing on the case of a cosmological phase transition, I will talk about how such anisotropies can give us a powerful probe of primordial non-Gaussianities, complementary to current and future CMB and LSS searches. In the scenario where astrophysical foregrounds are also present, I will then discuss some strategies using which we can extract the cosmological signal, focusing on the case of LISA, Taiji and BBO, in particular.

10:30–11:00 am
Jessica Howard
(Virtual via Zoom)
Title: Dark Matter Freeze-out during SU(2)_L Confinement
Abstract: We explore the possibility that dark matter is a pair of SU(2)_L doublets and propose a novel mechanism of dark matter production that proceeds through the confinement of the weak sector of the Standard Model. This phase of confinement causes the Standard Model doublets and dark matter to confine into pion-like objects. Before the weak sector deconfines, the dark pions freezeout and generate a relic abundance of dark matter. We solve the Boltzmann equations for this scenario to determine the scale of confinement and constituent dark matter mass required to produce the observed relic density. We determine which regions of this parameter space evade direct detection and collider bounds.

11:00–11:30 am
Juven Wang
Title: Quantum Matter Adventure to Beyond the Standard Model Prediction
Abstract: Ideas developed from the quantum matter and quantum field theory frontier may guide us to explore new physics beyond the 4d Standard Model. I propose a few such ideas. First, new physics for neutrinos: right-handed neutrinos carry a Z_{16} class mixed gauge-gravitational global anomaly index, which could be replaced by 4d or 5d topological quantum field theory, or 4d interacting conformal field theory. These theories provide possible new neutrino mass mechanisms [arXiv:2012.15860]. Second, deconfined quantum criticality between Grand Unified Theories: dictated by a Z_2 class global anomaly, a gapless quantum critical region can happen between Georgi-Glashow and Pati-Salam models as deformation of the Standard Model, where Beyond the Standard Model physics and Dark Gauge sector occur as neighbor phases [arXiv:2106.16248, arXiv:2112.14765, arXiv:2204.08393]. Third, the Strong CP problem can be solved by a new solution involving Symmetric Mass Generation [arXiv:2204.14271].

11:30–1:30 pm
Break

1:30–4:00 pm
Stephen R. Taylor
Title: Pulsar Timing Arrays: The Next Window onto the Low-frequency Gravitational-wave Universe
Abstract: The nanohertz-frequency band of gravitational waves should be awash with signals from supermassive black-hole binaries, as well as cosmological signatures of phase transitions, cosmic strings, and other relics of the early Universe. Pulsar-timing arrays (PTAs) like the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and the International Pulsar Timing Array are poised to chart this new frontier of gravitational wave discovery within the next several years. I will present exciting new results from recent cutting-edge searches, discuss some milestones on the road to the next decade of PTA discovery, and take workshop attendees through a guided tutorial of how the broader community can use our production-level analysis pipeline to extract new science with ease.

Friday, August 5, 2022

9:00–9:30 am
Breakfast

9:30–10:00 am
Ofri Telem
Title: Charge-Monopole Pairwise Phases from Dressed Quantum States

10:00–10:30 am
Sungwoo Hong
Title: Coupling a Cosmic String to a TQFT
Abstract: In the last few years, the notion of symmetry has been enlarged to “generalized symmetry” or “higher-form symmetry” and these more generalized symmetries have played a critical role in deepening our understanding of QFT, notably IR phases of QFT. In this talk, I will discuss a various ways of coupling the axion-Maxwell theory to a topological field theory (TQFT). Contrary to a common wisdom, I will show that such topological modifications can lead to direct changes in the local physics with possible observable consequences. This surprise can be realized by a dimensional reduction, namely, a coupling to a TQFT in 4d leads to a non-trivial and local impact on the 2d string world-sheet QFT. There also exists a topological modification of the theory, i.e. gauging a discrete subgroup of 0-form shift symmetry, and this time it results in a alteration of spectrum of cosmic strings. If time permits, I will also discuss generalized symmetries and associated higher-groups of these theories.

10:30–11:00 am
Eleanor Hall
(Virtual via Zoom)
Title: Non-perturbative methods for false vacuum decay
Abstract: Gravitational waves from phase transitions in the early universe are one of our most promising signal channels of BSM physics; however, existing methods for predicting these signals are limited to weakly-coupled theories. In this talk, I present the quasi-stationary effective action, a new non-perturbative formalism for false vacuum decay that integrates over local fluctuations in field space using the functional renormalization group. This method opens the door to reliable calculation of gravitational wave signals and false vacuum decay rates for strongly-interacting theories. I will also discuss recent developments and ongoing extensions of the QSEA.

11:00–1:30 pm
Break

1:30–2:00 pm
Mrunal Korwar
Title: Electroweak Symmetric Balls
Abstract: Electroweak symmetric balls are macroscopic objects with electroweak symmetry restored inside. Such an object can arise in models where dark sectors contain monopole or non-topological soliton with a Higgs portal interaction to the Standard Model. It could be produced in the early universe via phase transition or parametric resonance, accounting for all dark matter. In a scenario where the balls are allowed to evaporate, the observed baryon asymmetry in our universe could be explained by a mechanism of “catalyzed baryogenesis.” In this mechanism, the motion of a ball-like catalyst provides the necessary out-of-equilibrium condition, its outer wall has CP-violating interactions with the Standard Model particles, and its interior has baryon number violating interactions via electroweak Sphaleron. Because of electroweak symmetric cores, such objects have a large geometric cross-section off a nucleus, generating a multi-hit signature in large volume detectors. These objects could radiatively capture a nucleus and release GeV-scale energy for each interaction. The IceCube detector can probe dark matter balls with masses up to a gram.

2:00–2:30 pm
Seth Koren
Title: Discrete Gauged Baryon Minus Lepton Number and the Cosmological Lithium Problem
Abstract: We study the baryon minus lepton number gauge theory broken by a scalar with charge six. The infrared discrete vestige of the gauge symmetry demands the existence of cosmic string solutions, and their production as dynamical objects in the early universe is guaranteed by causality. These topological defects can support interactions which convert three protons into three positrons, and we argue an `electric’-`magnetic’ interplay can lead to an amplified, strong-scale cross-section in an analogue of the Callan-Rubakov effect.
The cosmological lithium problem—that theory predicts a primordial abundance thrice as high as that observed—has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We suggest cosmic strings have disintegrated O(1) of the primordial lithium nuclei and estimate the rate in a benchmark scenario. To our knowledge this is the first new physics mechanism with microphysical justification for the abundance of lithium uniquely to be modified after Big Bang Nucleosynthesis.

2:30–3:00 pm
Yann Gouttenoire
Title: Supercool Composite Dark Matter beyond 100 TeV

Advances in Mathematical Physics
2022-07-30 09:00 - 2022-08-01 13:45 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
A Conference in Honor of Elliott H. Lieb on his 90th Birthday
On July 30 – Aug 1, 2022 the Harvard Mathematics Department and the CMSA co-hosted a birthday conference in honor of Elliott Lieb.
This meeting highlights Elliott’s vast contribution to math and physics. Additionally, this meeting features Prof. Lieb’s more recent impact in strong subadditivity of entropy and integrable systems (ice model, Temperley-Lieb algebra etc.).
Venue:
July 30–31, 2022: Hall B, Science Center, 1 Oxford Street, Cambridge, MA, 02138
August 1, 2022: Hall C, Science Center, 1 Oxford Street, Cambridge, MA, 02138
Schedule (pdf)
Organizers:
Michael Aizenman, Princeton University
Joel Lebowitz, Rutgers University
Ruedi Seiler, Technische Universität Berlin
Herbert Spohn, Technical University of Munich
Horng-Tzer Yau, Harvard University
Shing-Tung Yau, Harvard University
Jakob Yngvason, University of Vienna
SPEAKERS:
Rafael Benguria, Pontificia Universidad Catolica de Chile
Eric Carlen, Rutgers University
Philippe Di Francesco, University of Illinois
Hugo Duminil-Copin, IHES
László Erdös, Institute of Science and Technology Austria
Rupert Frank, Ludwig Maximilian University of Munich
Jürg Fröhlich, ETH Zurich
Alessandro Giuliani, Università degli Studi Roma Tre
Bertrand Halperin, Harvard University
Klaus Hepp, Institute for Theoretical Physics, ETH Zurich
Sabine Jansen, Ludwig Maximilian University of Munich
Mathieu Lewin, Université Paris-Dauphine
Bruno Nachtergaele, The University of California, Davis
Yoshiko Ogata, University of Tokyo
Ron Peled, Tel Aviv University
Benjamin Schlein, University of Zurich
Robert Seiringer, Institute of Science and Technology Austria
Jan Philip Solovej, University of Copenhagen
Hal Tasaki, Gakushuin University
Simone Warzel, Technical University of Munich
Jun Yin, The University of California, Los Angeles

Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data
2022-07-28 09:00 - 10:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Interdisciplinary Science Seminar
Speaker: Sumit Sinha, Harvard University
Title: Statistical Mechanical theory for spatio-temporal evolution of Intra-tumor heterogeneity in cancers: Analysis of Multiregion sequencing data (https://arxiv.org/abs/2202.10595)
Abstract: Variations in characteristics from one region (sub-population) to another are commonly observed in complex systems, such as glasses and a collection of cells. Such variations are manifestations of heterogeneity, whose spatial and temporal behavior is hard to describe theoretically. In the context of cancer, intra-tumor heterogeneity (ITH), characterized by cells with genetic and phenotypic variability that co-exist within a single tumor, is often the cause of ineffective therapy and recurrence of cancer. Next-generation sequencing, obtained by sampling multiple regions of a single tumor (multi-region sequencing, M-Seq), has vividly demonstrated the pervasive nature of ITH, raising the need for a theory that accounts for evolution of tumor heterogeneity. Here, we develop a statistical mechanical theory to quantify ITH, using the Hamming distance, between genetic mutations in distinct regions within a single tumor. An analytic expression for ITH, expressed in terms of cell division probability (α) and mutation probability (p), is validated using cellular-automaton type simulations. Application of the theory successfully captures ITH extracted from M-seq data in patients with exogenous cancers (melanoma and lung). The theory, based on punctuated evolution at the early stages of the tumor followed by neutral evolution, is accurate provided the spatial variation in the tumor mutation burden is not large. We show that there are substantial variations in ITH in distinct regions of a single solid tumor, which supports the notion that distinct subclones could co-exist. The simulations show that there are substantial variations in the sub-populations, with the ITH increasing as the distance between the regions increases. The analytical and simulation framework developed here could be used in the quantitative analyses of the experimental (M-Seq) data. More broadly, our theory is likely to be useful in analyzing dynamic heterogeneity in complex systems such as supercooled liquids.
Bio: I am a postdoctoral fellow in Harvard SEAS (Applied Mathematics) and Dana Farber Cancer Institute (Data Science) beginning Feb 2022. I finished my PhD in Physics (Theoretical Biophysics) from UT Austin (Jan 2022) on “Theoretical and computational studies of growing tissue”. I pursued my undergraduate degree in Physics from the Indian Institute of Technology, Kanpur in India (2015). Boradly, I am interested in developing theoretical models, inspired from many-body statistical physics, for biological processes at different length and time scales.
