Calendar

On Monday, May 3rd the Harvard CMSA will be hosting a Computational Biology Symposium virtually on Zoom. Please visit the event webpage for the schedule and more information. The event poster is attached.

Registration is free but required. Register here. Details on how to join the webinar will be sent to registered participants before the event.

The speakers will be:
Uri Alon, Weizmann Institute
Elana Fertig, Johns Hopkins
Martin Hemberg, Brigham and Women’s Hospital
Peter Kharchenko, Harvard University
Smita Krishnaswamy, Yale University
John Marioni, EMBL-EBI
Eran Segal, Weizmann Institute
Meromit Singer, Harvard Medical School

Lieb-Thirring inequalities are a mathematical expression of the uncertainty and exclusion principles in quantum mechanics. They were introduced by Lieb and Thirring in 1975 in their proof of stability of matter and have since played an important role in several areas of analysis and mathematical physics. We provide a gentle introduction to classical aspects of this subject and we also present some newer developments, concerning extensions of several inequalities in harmonic analysis to the setting of families of orthonormal functions.

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

In 1948 Hoeffding proposed a nonparametric test that detects dependence between two continuous random variables (X,Y), based on the ranking of n paired samples (Xi,Yi). The computation of this commonly-used test statistic requires O(n log n) time. Hoeffding’s test is consistent against any dependent probability density f(x,y), but can be fooled by other bivariate distributions with continuous margins. Variants of this test with stronger consistency have been considered in works by Blum, Kiefer, and Rosenblatt, Yanagimoto, and Bergsma and Dassios, and others. The so far best known algorithms to compute them have required quadratic time.

We present an algorithm that computes these improved tests in time O(n log n). It is based on a new combinatorial approach for counting pattern occurrences in a given permutation, which we call corner tree formulas, and will be explained in the talk.

Joint work with Calvin Leng.

Zoom: https://harvard.zoom.us/j/98231541450

We introduce refined unramified cohomology and prove some
general comparison theorems to cycle groups. Our approach has several applications. For instance, it allows to construct the first example of a smooth complex projective variety whose Griffiths group has infinite torsion subgroup.

Zoom: https://harvard.zoom.us/j/91794282895?pwd=VFZxRWdDQ0VNT0hsVTllR0JCQytoZz09

We are interested in smoothing of a degenerate Calabi-Yau variety or a pair (degenerate CY, sheaf). I will explain an algebraic framework for solving such smoothability problems. The idea is to glue local dg Lie algebras (or dg Batalin-Vilkovisky algebras), coming from suitable local models, to get a global object. The key observation is that while this object is only an almost dg Lie algebra (or pre-dg Lie algebra), it is sufficient to prove unobstructedness of the associated Maurer-Cartan equation (a kind of Bogomolov-Tian-Todorov theorem) under suitable assumptions, so the former can be regarded as a singular version of the Kodaira-Spencer DGLA. Our framework applies to degenerate CY varieties previously studied by Kawamata-Namikawa and Gross-Siebert, as well as a more general class of varieties called toroidal crossing spaces (by the recent work of Felten-Filip-Ruddat). This talk is based on joint works with Conan Leung, Ziming Ma and Y.-H. Suen.

Zoom: https://harvard.zoom.us/j/96709211410?pwd=SHJyUUc4NzU5Y1d0N2FKVzIwcmEzdz09

Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.

Zoom: https://harvard.zoom.us/j/977347126

In this expository talk, I’ll use 1d voter models to illustrate basic features of neutral theory—a vision of how genetic and ecological diversity can emerge even without selective pressure. We’ll see how questions about the persistence and spatial organization of lineages can be rephrased, in these models, as questions about random walks.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

In this talk, I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.

Zoom: https://harvard.zoom.us/j/977347126

The aim of the workshop is to bring together a community of researchers in mathematics, computer science and data science who develop theoretical and computational models to characterize shapes and analysis of image data.

The first half of the workshop will feature talks aimed at graduate students, newcomers and a broad spectrum of audiences. Christopher Bishop (Stony Brook) and Keenan Crane (Carnegie Mellon) will each give two featured talks. The remaining part will have both background and research talks. There will also be organized discussions of open problems and potential applications.

Register here to attend this event

To find out details about the event, visit the CMSA event page.

This talk is about learning from informant, a formal model for binary classification. Illustrating examples are linear separators and other uniformly decidable sets of formal languages. Due to the learning by enumeration technique by Gold the learning process can be assumed consistent when full-information is available.
The original model can be adjusted towards the setting of deep learning. We investigate the learnability of the set of half-spaces by these incremental learners. Moreover, they have less learning power than the full-information variant by a fundamental proof technique due to Blum and Blum. This technique can also be used to separate consistency.
Finally, we present recent results towards a better understanding of (strong) non-U-shaped learning from binary labeled input data. To separate the syntactic variant, we employ an infinite recursion theorem by Case.

Zoom: https://harvard.zoom.us/j/98231541450

Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.

Zoom: https://harvard.zoom.us/j/977347126

Submodular function maximization has been a central topic in the theoretical computer science community over the last decade. Plenty of well-performing approximation algorithms have been designed for the maximization of (monotone or non-monotone) submodular functions over a variety of constraints. In this talk, we consider the submodular multiple knapsack problem (SMKP), which is the submodular version of the well-studied multiple knapsack problem (MKP). Roughly speaking, the problem asks to maximize a monotone submodular function over multiple bins (knapsacks). Recently, Fairstein et al. (ESA20) presented a tight (1−1/e−ϵ)-approximation randomized algorithm for SMKP. Their algorithm is based on the continuous greedy technique which inherently involves randomness. However, the deterministic algorithm of this problem has not been understood very well previously. In this paper, we present a tight (1−1/e−ϵ) deterministic algorithm for SMKP. Our algorithm is based on reducing SMKP to an exponential-size submodular maximizaion problem over a special partition matroid which enjoys a tight deterministic algorithm. We develop several techniques to mimic the algorithm, leading to a tight deterministic approximation for SMKP.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement.
As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalizing the Nielsen-Ninomiya theorem.
Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D.
Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture.
The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].

Zoom: https://harvard.zoom.us/j/977347126

One of the hottest sub-topics of machine learning in recent times has been Self-Supervised Learning (SSL). In SSL, a learning machine captures the dependencies between input variables, some of which may be observed, denoted X, and others not always observed, denoted Y. SSL pre-training has revolutionized natural language processing and is making very fast progress in speech and image recognition. SSL may enable machines to learn predictive models of the world through observation, and to learn representations of the perceptual world, thereby reducing the number of labeled samples or rewarded trials to learn a downstream task. In the Energy-Based Model framework (EBM), both X and Y are inputs, and the model outputs a scalar energy that measures the degree of incompatibility between X and Y. EBMs are implicit functions that can represent complex and multimodal dependencies between X and Y. EBM architectures belong to two main families: joint embedding architectures and latent-variable generative architectures. There are two main families of methods to train EBMs: contrastive methods, and volume regularization methods. Much of the underlying mathematics of EBM is borrowed from statistical physics, including concepts of partition function, free energy, and variational approximations thereof.

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

Several optimization problems in AI Machine Learning can be solved with the maximization of functions that exhibit natural diminishing returns. Examples include feature selection for Generalized Linear Models, Data Summarization, and Bayesian experimental design. By leveraging diminishing returns, it is possible to design efficient approximation algorithms for these problems.One of the simplest notions of diminishing returns is submodularity. Submodular functions are particularly interesting, because they admit simple, yet non-trivial, polynomial-time approximation algorithms. In recent years, several definitions have been proposed, to generalize the notion of submodularity. A study of these generalized functions lead to the design of efficient approximation algorithms for non-convex problems.In this talk, I will discuss the notion of submodularity, and illustrate relevant results on this topic, including new interesting combinatorial algorithms. I will also talk about generalizations of this notion to continuous domains, and how they translate into first- and second-order conditions. I will discuss how these notions pertain interesting problems in AI Machine Learning.

Zoom: https://harvard.zoom.us/j/98231541450

The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided.

The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.

Zoom: https://harvard.zoom.us/j/977347126

The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided.

The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.

Zoom: https://harvard.zoom.us/j/977347126

Proteolysis-targeting chimeras (PROTACs) are heterobifunctional small molecules consisting of two chemical moieties connected by a linker.  The simultaneous binding of a PROTAC to both a target protein and an E3 ligase facilitates ubiquitination and degradation of the target protein. Since its proof-of-concept research in 2001, PROTAC has been vigorously developed by both research community and pharma industry, to act against therapeutically significant proteins, such as BRD4, BTK, and STAT3. However, despite the enthusiasm, designing PROTACs is challenging. Till now, no case of de novo rational design of PROTACs has been reported and the successful PROTACs usually came from the functional screen from a limitedly scaled library.  As formation of a ternary complex between the protein target, the PROTAC, and the recruited E3 ligase is considered paramount for successful degradation, several computational algorithms (PRosettaC as the example), have been developed to model this ternary complex, which have got partial agreement with the experimental data and in principle inform future rational PROTAC design. Here I will introduce some of these computational methods and share how they model the ternary complexes.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)

Zoom: https://harvard.zoom.us/j/977347126

TITLE: K-theory and characteristic classes in topology and complex geometry (a tribute to Atiyah and Hirzebruch)

ABSTRACT: We will discuss the K-theory of complex vector bundles on
topological spaces and of holomorphic vector bundles on complex
manifolds. A central question is the relationship between K-theory
and cohomology. This is done in topology by constructing
characteristic classes, but other constructions appear in the

holomorphic or algebraic context. We will discuss the Hirzebruch-
Riemann-Roch formula, the Atiyah-Hirzebruch spectral sequence, the

role of complex cobordism, and other tools developed later on, like
the Bloch-Ogus spectral sequence.

Talk chair: Baohua Fu

Written articles will accompany each lecture in this series and be available as part of the publication “History and Literature of Mathematical Science.”

For more information, please visit the event page.

Register here to attend.

We will present some rigorous results about Relative entropy in QFT, motivated in part by recent physicists’ work which however depends on heuristic arguments such as introducing cut off and using path integrals. In the particular case of CFT, we will discuss interesting relations between relative entropy, central charge and global dimension of conformal net

Zoom: https://harvard.zoom.us/j/779283357?pwd=MitXVm1pYUlJVzZqT3lwV2pCT1ZUQT09

Title: New Structures in Gravitational Waves

Abstract: Mathematical General Relativity (GR) explores the structures and resulting dynamics of gravitational systems. These are described by the Einstein equations, which can be written as a system of nonlinear, hyperbolic partial differential equations. Recent years have seen fruitful interactions between physical questions and geometric analysis, sparking new breakthroughs, in particular related to gravitational radiation. Gravitational waves transport information from faraway regions of the Universe. They were observed for the first time by Advanced LIGO in 2015. So far, most studies in GR have been devoted to sources like binary black hole mergers or generally to sources that are stationary outside of a compact set. However, when extended neutrino halos are present, the situation changes.  Mathematically, we describe these systems by asymptotically-flat manifolds solving the Einstein equations. In this talk, I will present new results on gravitational radiation for sources that are not stationary outside of a compact set, but whose gravitational fields fall off more slowly towards infinity. A panorama of new gravitational effects opens up when delving deeper into these more general spacetimes. In particular, whereas the former sources produce memory effects (permanent change of the spacetime) that are finite and of purely electric parity, the latter in addition generate memory of magnetic type, and both types grow. These new effects emerge naturally from the Einstein equations.

Registration is required to receive the Zoom information.

Please go here to register.

Information visualizations are an efficient means to support the users in understanding large amounts of complex, interconnected data; user comprehension. Previous research suggests that user-adaptive information visualizations positively impact the users’ performance in visualization tasks. This study aims to develop a computational model to predict the users’ success in visual search tasks from eye gaze data and thereby drive such user-adaptive systems. State-of-the-art deep learning models for time series classification have been trained on sequential eye gaze data obtained from 40 study participants’ interaction with a circular and an organizational graph. The results suggest that such models yield higher accuracy than a baseline classifier and previously used models for this purpose. In particular, a Multivariate Long Short Term Memory Fully Convolutional Network (MLSTM-FCN) shows encouraging performance for its use in on-line user-adaptive systems. Given this finding, such a computational model can infer the users’ need for support during interaction with a graph and trigger appropriate interventions in user-adaptive information visualization systems.

Zoom: https://harvard.zoom.us/j/98248914765?pwd=Q01tRTVWTVBGT0lXek40VzdxdVVPQT09

(Password: 419419)