Deregulation through Direct Democracy: Lessons from Liquor
2019-04-03 14:30 - 15:30 (America/New_York) | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Sarah Moshary (University of Chicago)
Title: Deregulation through Direct Democracy: Lessons from Liquor
Abstract: This paper examines the merits of state control versus private provision of spirits retail, using the 2012 deregulation of liquor sales in Washington state as an event study. We document effects along a number of dimensions: prices, product variety, convenience, substitution to other goods, state revenue, and consumption externalities. We estimate a demand system to evaluate the net effect of privatization on consumer welfare. Our findings suggest that deregulation harmed the median Washingtonian, even though residents voted in favor of deregulation by a 16% margin. Further, we find that vote shares for the deregulation initiative do not reflect welfare gains at the ZIP code level. We discuss implications of our findings for the efficacy of direct democracy as a policy tool.

4/3/2019 Fluid Dynamics Seminar
2019-04-03 20:54 | MA

4/4/2019 General Relativity Seminar
2019-04-04 15:30 - 16:30 | MA

4/4/2019 Random Matrix and Probability Theory Seminar
2019-04-04 16:30 - 17:30 | MA

4/8/2019 Mathematical Physics Seminar
2019-04-08 12:00 - 13:00 | MA

Math Science Lectures in Honor of Raoul Bott: Mina Aganagic
2019-04-09 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On April 9 and 10, 2019 the CMSA hosted two lectures by Mina Aganagic (UC Berkeley). This was the second annual Math Science Lecture Series held in honor of Raoul Bott.
The lectures took place in Science Center, Hall C
“Two math lessons from string theory”

April 9, 2019
Lecture 1
Title: “Lesson on Integrability”
Abstract: The quantum Knizhnik-Zamolodchikov (qKZ) equation is a difference generalization of the famous Knizhnik-Zamolodchikov (KZ) equation. The problem to explicitly capture the monodromy of the qKZ equation has been open for over 25 years. I will describe the solution to this problem, discovered jointly with Andrei Okounkov. The solution comes from the geometry of Nakajima quiver varieties and has a string theory origin.
Part of the interest in the qKZ monodromy problem is that its solution leads to integrable lattice models, in parallel to how monodromy matrices of the KZ equation lead to knot invariants. Thus, our solution of the problem leads to a new, geometric approach, to integrable lattice models. There are two other approaches to integrable lattice models, due to Nekrasov and Shatashvili and to Costello, Witten and Yamazaki. I’ll describe joint work with Nikita Nekrasov which explains how string theory unifies the three approaches to integrable lattice models.

April 10, 2019
Lecture 2
Title: “Lesson on Knot Categorification”
Abstract: An old problem is to find a unified approach to the knot categorification problem. The new string theory perspective on the qKZ equation I described in the first talk can be used to derive two geometric approaches to the problem.
The first approach is based on a category of B-type branes on resolutions of slices in affine Grassmannians. The second is based on a category of A-branes in a Landau-Ginzburg theory. The relation between them is two dimensional (equivariant) mirror symmetry. String theory also predicts that a third approach to categorification, based on counting solutions to five dimensional Haydys-Witten equations, is equivalent to the first two.
This talk is mostly based on joint work with Andrei Okounkov.

Inequality Aversion, Populism, and the Backlash Against Globalization
2019-04-10 14:30 - 15:30 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Pietro Veronesi (University of Chicago)
Title: Inequality Aversion, Populism, and the Backlash Against Globalization
Abstract: Motivated by the recent rise of populism in western democracies, we develop a model in which a populist backlash emerges endogenously in a growing economy. In the model, voters dislike inequality, especially the high consumption of “elites.” Economic growth exacerbates inequality due to heterogeneity in risk aversion. In response to rising inequality, rich-country voters optimally elect a populist promising to end globalization. Countries with more inequality, higher financial development, and current account deficits are more vulnerable to populism, both in the model and in the data. Evidence on who voted for Brexit and Trump in 2016 also supports the model.

4/11/2019 Random Matrix and Probability Theory Seminar
2019-04-11 16:30 - 17:30 | MA

Workshop on Invariance and Geometry in Sensation, Action and Cognition
2019-04-15 09:15 - 2019-04-17 16:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
As part of the program on Mathematical Biology a workshop on Invariance and Geometry in Sensation, Action and Cognition will take place on April 15-17, 2019.
Legend has it that above the door to Plato’s Academy was inscribed “Μηδείς άγεωµέτρητος είσίτω µον τήν στέγην”, translated as “Let no one ignorant of geometry enter my doors”. While geometry and invariance has always been a cornerstone of mathematics, it has traditionally not been an important part of biology, except in the context of aspects of structural biology. The premise of this meeting is a tantalizing sense that geometry and invariance are also likely to be important in (neuro)biology and cognition. Since all organisms interact with the physical world, this implies that as neural systems extract information using the senses to guide action in the world, they need appropriately invariant representations that are stable, reproducible and capable of being learned. These invariances are a function of the nature and type of signal, its corruption via noise, and the method of storage and use.
This hypothesis suggests many puzzles and questions: What representational geometries are reflected in the brain? Are they learned or innate? What happens to the invariances under realistic assumptions about noise, nonlinearity and finite computational resources? Can cases of mental disorders and consequences of brain damage be characterized as break downs in representational invariances? Can we harness these invariances and sensory contingencies to build more intelligent machines? The aim is to revisit these old neuro-cognitive problems using a series of modern lenses experimentally, theoretically and computationally, with some tutorials on how the mathematics and engineering of invariant representations in machines and algorithms might serve as useful null models.
In addition to talks, there will be a set of tutorial talks on the mathematical description of invariance (P.J. Olver), the computer vision aspects of invariant algorithms (S. Soatto), and the neuroscientific and cognitive aspects of invariance (TBA). The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA. This workshop is organized by L. Mahadevan (Harvard), Talia Konkle (Harvard), Samuel Gershman (Harvard), and Vivek Jayaraman (HHMI).
Videos
Tentative Speaker List:

Alessandro Achille, UCLA
Vijay Balasubramanian, University of Pennsylvania
Jeannette Bohg, Stanford
Ed Connor, Johns Hopkins
Moira Dillon, NYU
Jacob Feldman, Rutgers
Ila Fiete, MIT
Sam Gershman, Harvard
Gily Ginosar, Weizmann Institute of Science
Lucia Jacobs, UC Berkeley
Vivek Jayaraman, HHMI
Talia Konkle, Harvard
L. Mahadevan, Harvard
Michael McCloskey, Johns Hopkins
Sam Ocko, Stanford
Peter Olver, University of Minnesota
Anitha Pasupathy, University of Washington
Sandro Romani, Janelia
Stefano Soatto, UCLA
Tatyana Sharpee, Salk Institute
Dagmar Sternad, Northeastern
Elizabeth Torres, Rutgers

Schedule:
Monday, April 15

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 9:15am
Welcome and Introduction

9:15 – 10:00am
Vivek Jayaraman
Title: Insect cognition: Small tales of geometry & invariance
Abstract: Decades of field and laboratory experiments have allowed ethologists to discover the remarkable sophistication of insect behavior. Over the past couple of decades, physiologists have been able to peek under the hood to uncover sophistication in insect brain dynamics as well. In my talk, I will describe phenomena that relate to the workshop’s theme of geometry and invariance. I will outline how studying insects —and flies in particular— may enable an understanding of the neural mechanisms underlying these intriguing phenomena.

10:00 – 10:45am
Elizabeth Torres
Title: Connecting Cognition and Biophysical Motions Through Geometric Invariants and Motion Variability
Abstract: In the 1930s Nikolai Bernstein defined the degrees of freedom (DoF) problem. He asked how the brain could control abundant DoF and produce consistent solutions, when the internal space of bodily configurations had much higher dimensions than the space defining the purpose(s) of our actions. His question opened two fundamental problems in the field of motor control. One relates to the uniqueness or consistency of a solution to the DoF problem, while the other refers to the characterization of the diverse patterns of variability that such solution produces.
In this talk I present a general geometric solution to Bernstein’s DoF problem and provide empirical evidence for symmetries and invariances that this solution provides during the coordination of complex naturalistic actions. I further introduce fundamentally different patterns of variability that emerge in deliberate vs. spontaneous movements discovered in my lab while studying athletes and dancers performing interactive actions. I here reformulate the DoF problem from the standpoint of the social brain and recast it considering graph theory and network connectivity analyses amenable to study one of the most poignant developmental disorders of our times: Autism Spectrum Disorders.
I offer a new unifying framework to recast dynamic and complex cognitive and social behaviors of the full organism and to characterize biophysical motion patterns during migration of induced pluripotent stem cell colonies on their way to become neurons.

10:45 – 11:15am
Coffee Break

11:15 – 12:00pm
Peter Olver
Title: Symmetry and invariance in cognition — a mathematical perspective”
Abstract: Symmetry recognition and appreciation is fundamental in human cognition. (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance. Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones. Mathematical prerequisites will be kept to a bare minimum.

12:00 – 12:45pm
Stefano Soatto/Alessandro Achille
Title: Information in the Weights and Emergent Properties of Deep Neural Networks
Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.
While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

12:45 – 2:00pm
Lunch

2:00 – 2:45pm
Anitha Pasupathy
Title: Invariant and non-invariant representations in mid-level ventral visual cortex
My laboratory investigates how visual form is encoded in area V4, a critical mid-level stage of form processing in the macaque monkey. Our goal is to reveal how V4 representations underlie our ability to segment visual scenes and recognize objects. In my talk I will present results from two experiments that highlight the different strategies used by the visual to achieve these goals. First, most V4 neurons exhibit form tuning that is exquisitely invariant to size and position, properties likely important to support invariant object recognition. On the other hand, form tuning in a majority of neurons is also highly dependent on the interior fill. Interestingly, unlike primate V4 neurons, units in a convolutional neural network trained to recognize objects (AlexNet) overwhelmingly exhibit fill-outline invariance. I will argue that this divergence between real and artificial circuits reflects the importance of local contrast in parsing visual scenes and overall scene understanding.

2:45 – 3:30pm
Jacob Feldman
Title: Bayesian skeleton estimation for shape representation and perceptual organization
Abstract: In this talk I will briefly summarize a framework in which shape representation and perceptual organization are reframed as probabilistic estimation problems. The approach centers around the goal of identifying the skeletal model that best “explains” a given shape. A Bayesian solution to this problem requires identifying a prior over shape skeletons, which penalizes complexity, and a likelihood model, which quantifies how well any particular skeleton model fits the data observed in the image. The maximum-posterior skeletal model thus constitutes the most “rational” interpretation of the image data consistent with the given assumptions. This approach can easily be extended and generalized in a number of ways, allowing a number of traditional problems in perceptual organization to be “probabilized.” I will briefly illustrate several such extensions, including (1) figure/ground and grouping (3) 3D shape and (2) shape similarity.

3:30 – 4:00pm
Tea Break

4:00 – 4:45pm
Moira Dillon
Title: Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development
Abstract: Formal geometry lies at the foundation of millennia of human achievement in domains such as mathematics, science, and art. While formal geometry’s propositions rely on abstract entities like dimensionless points and infinitely long lines, the points and lines of our everyday world all have dimension and are finite. How, then, do we get to abstract geometric thought? In this talk, I will provide evidence that evolutionarily ancient and developmentally precocious sensitivities to the geometry of our everyday world form the foundation of, but also limit, our mathematical reasoning. I will also suggest that successful geometric reasoning may emerge through development when children abandon incorrect, axiomatic-based strategies and come to rely on dynamic simulations of physical entities. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

4:45 – 5:30pm
Michael McCloskey
Title: Axes and Coordinate Systems in Representing Object Shape and Orientation
Abstract: I describe a theoretical perspective in which a) object shape is represented in an object-centered reference frame constructed around orthogonal axes; and b) object orientation is represented by mapping the object-centered frame onto an extrinsic (egocentric or environment-centered) frame. I first show that this perspective is motivated by, and sheds light on, object orientation errors observed in neurotypical children and adults, and in a remarkable case of impaired orientation perception. I then suggest that orientation errors can be used to address questions concerning how object axes are defined on the basis of object geometry—for example, what aspects of object geometry (e.g., elongation, symmetry, structural centrality of parts) play a role in defining an object principal axis?

5:30 – 6:30pm
Reception

Tuesday, April 16

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 9:45am
Peter Olver
Title: Symmetry and invariance in cognition — a mathematical perspective”
Abstract: Symmetry recognition and appreciation is fundamental in human cognition. (It is worth speculating as to why this may be so, but that is not my intent.) The goal of these two talks is to survey old and new mathematical perspectives on symmetry and invariance. Applications will arise from art, computer vision, geometry, and beyond, and will include recent work on 2D and 3D jigsaw puzzle assembly and an ongoing collaboration with anthropologists on the analysis and refitting of broken bones. Mathematical pre

9:45 – 10:30am
Stefano Soatto/Alessandro Achille
Title: Information in the Weights and Emergent Properties of Deep Neural Networks
Abstract: We introduce the notion of information contained in the weights of a Deep Neural Network and show that it can be used to control and describe the training process of DNNs, and can explain how properties, such as invariance to nuisance variability and disentanglement, emerge naturally in the learned representation. Through its dynamics, stochastic gradient descent (SGD) implicitly regularizes the information in the weights, which can then be used to bound the generalization error through the PAC-Bayes bound. Moreover, the information in the weights can be used to defined both a topology and an asymmetric distance in the space of tasks, which can then be used to predict the training time and the performance on a new task given a solution to a pre-training task.
While this information distance models difficulty of transfer in first approximation, we show the existence of non-trivial irreversible dynamics during the initial transient phase of convergence when the network is acquiring information, which makes the approximation fail. This is closely related to critical learning periods in biology, and suggests that studying the initial convergence transient can yield important insight beyond those that can be gleaned from the well-studied asymptotics.

10:30 – 11:00am
Coffee Break

11:00 – 11:45am
Jeannette Bohg
Title: On perceptual representations and how they interact with actions and physical representations
Abstract: I will discuss the hypothesis that perception is active and shaped by our task and our expectations on how the world behaves upon physical interaction. Recent approaches in robotics follow this insight that perception is facilitated by physical interaction with the environment. First, interaction creates a rich sensory signal that would otherwise not be present. And second, knowledge of the regularity in the combined space of sensory data and action parameters facilitate the prediction and interpretation of the signal. In this talk, I will present two examples from our previous work where a predictive task facilitates autonomous robot manipulation by biasing the representation of the raw sensory data. I will present results on visual but also haptic data.

11:45 – 12:30pm
Dagmar Sternad
Title: Exploiting the Geometry of the Solution Space to Reduce Sensitivity to Neuromotor Noise
Abstract: Control and coordination of skilled action is frequently examined in isolation as a neuromuscular problem. However, goal-directed actions are guided by information that creates solutions that are defined as a relation between the actor and the environment. We have developed a task-dynamic approach that starts with a physical model of the task and mathematical analysis of the solution spaces for the task. Based on this analysis we can trace how humans develop strategies that meet complex demands by exploiting the geometry of the solution space. Using three interactive tasks – throwing or bouncing a ball and transporting a “cup of coffee” – we show that humans develop skill by: 1) finding noise-tolerant strategies and channeling noise into task-irrelevant dimensions, 2) exploiting solutions with dynamic stability, and 3) optimizing predictability of the object dynamics. These findings are the basis for developing propositions about the controller: complex actions are generated with dynamic primitives, attractors with few invariant types that overcome substantial delays and noise in the neuro-mechanical system.

12:30 – 2:00pm
Lunch

2:00 – 2:45pm
Sam Ocko
Title: Emergent Elasticity in the Neural Code for Space
Abstract: To navigate a novel environment, animals must construct an internal map of space by combining information from two distinct sources: self-motion cues and sensory perception of landmarks. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to construct such internal maps, and how are these maps used to maintain representations of an animal’s position within an environment. We demonstrate analytically how a neural attractor model that combines path integration of self-motion with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent internal map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network during exploration. Moreover, we verify several experimentally testable predictions of our model, including: (1) systematic deformations of grid cells in irregular environments, (2) path-dependent shifts in grid cells towards the most recently encountered landmark, (3) a dynamical phase transition in which grid cells can break free of landmarks in altered virtual reality environments and (4) the creation of topological defects in grid cells. Taken together, our results conceptually link known biophysical aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

2:45 – 3:30pm
Tatyana Sharpee
Title: Hyperbolic geometry of the olfactory space
Abstract: The sense of smell can be used to avoid poisons or estimate a food’s nutrition content because biochemical reactions create many by-products. Thus, the production of a specific poison by a plant or bacteria will be accompanied by the emission of certain sets of volatile compounds. An animal can therefore judge the presence of poisons in the food by how the food smells. This perspective suggests that the nervous system can classify odors based on statistics of their co-occurrence within natural mixtures rather than from the chemical structures of the ligands themselves. We show that this statistical perspective makes it possible to map odors to points in a hyperbolic space. Hyperbolic coordinates have a long but often underappreciated history of relevance to biology. For example, these coordinates approximate distance between species computed along dendrograms, and more generally between points within hierarchical tree-like networks. We find that both natural odors and human perceptual descriptions of smells can be described using a three-dimensional hyperbolic space. This match in geometries can avoid distortions that would otherwise arise when mapping odors to perception. We identify three axes in the perceptual space that are aligned with odor pleasantness, its molecular boiling point and acidity. Because the perceptual space is curved, one can predict odor pleasantness by knowing the coordinates along the molecular boiling point and acidity axes.

3:30 – 4:00pm
Tea Break

4:00 – 4:45pm
Ed Connor
Title: Representation of solid geometry in object vision cortex
Abstract: There is a fundamental tension in object vision between the 2D nature of retinal images and the 3D nature of physical reality. Studies of object processing in the ventral pathway of primate visual cortex have focused mainly on 2D image information. Our latest results, however, show that representations of 3D geometry predominate even in V4, the first object-specific stage in the ventral pathway. The majority of V4 neurons exhibit strong responses and clear selectivity for solid, 3D shape fragments. These responses are remarkably invariant across radically different image cues for 3D shape: shading, specularity, reflection, refraction, and binocular disparity (stereopsis). In V4 and in subsequent stages of the ventral pathway, solid shape geometry is represented in terms of surface fragments and medial axis fragments. Whole objects are represented by ensembles of neurons signaling the shapes and relative positions of their constituent parts. The neural tuning dimensionality of these representations includes principal surface curvatures and their orientations, surface normal orientation, medial axis orientation, axial curvature, axial topology, and position relative to object center of mass. Thus, the ventral pathway implements a rapid transformation of 2D image data into explicit representations 3D geometry, providing cognitive access to the detailed structure of physical reality.

4:45 – 5:30pm
L. Mahadevan
Title: Simple aspects of geometry and probability in perception
Abstract: Inspired by problems associated with noisy perception, I will discuss two questions: (i) how might we test people’s perception of probability in a geometric context ? (ii) can one construct invariant descriptions of 2D images using simple notions of probabilistic geometry? Along the way, I will highlight other questions that the intertwining of geometry and probability raises in a broader perceptual context.

Wednesday, April 17

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 9:45am
Gily Ginosar
Title: The 3D geometry of grid cells in flying bats
Abstract: The medial entorhinal cortex (MEC) contains a variety of spatial cells, including grid cells and border cells. In 2D, grid cells fire when the animal passes near the vertices of a 2D spatial lattice (or grid), which is characterized by circular firing-fields separated by fixed distances, and 60 local angles – resulting in a hexagonal structure. Although many animals navigate in 3D space, no studies have examined the 3D volumetric firing of MEC neurons. Here we addressed this by training Egyptian fruit bats to fly in a large room (5.84.62.7m), while we wirelessly recorded single neurons in MEC. We found 3D border cells and 3D head-direction cells, as well as many neurons with multiple spherical firing-fields. 20% of the multi-field neurons were 3D grid cells, exhibiting a narrow distribution of characteristic distances between neighboring fields – but not a perfect 3D global lattice. The 3D grid cells formed a functional continuum with less structured multi-field neurons. Both 3D grid cells and multi-field cells exhibited an anatomical gradient of spatial scale along the dorso-ventral axis of MEC, with inter-field spacing increasing ventrally – similar to 2D grid cells in rodents. We modeled 3D grid cells and multi-field cells as emerging from pairwise-interactions between fields, using an energy potential that induces repulsion at short distances and attraction at long distances. Our analysis shows that the model explains the data significantly better than a random arrangement of fields. Interestingly, simulating the exact same model in 2D yielded a hexagonal-like structure, akin to grid cells in rodents. Together, the experimental data and preliminary modeling suggest that the global property of grid cells is multiple fields that repel each other with a characteristic distance-scale between adjacent fields – which in 2D yields a global hexagonal lattice while in 3D yields only local structure but no global lattice.
Gily Ginosar 1 , Johnatan Aljadeff 2 , Yoram Burak 3 , Haim Sompolinsky 3 , Liora Las 1 , Nachum Ulanovsky 1
(1) Department of Neurobiology, Weizmann Institute of Science, Rehovot 76100, Israel
(2) Department of Bioengineering, Imperial College London, London, SW7 2AZ, UK
(3) The Edmond and Lily Safra Center for Brain Sciences, and Racah Institute of Physics, The Hebrew
University of Jerusalem, Jerusalem, 91904, Israel

9:45 – 10:30am
Sandro Romani
Title: Neural networks for 3D rotations
Abstract: Studies in rodents, bats, and humans have uncovered the existence of neurons that encode the orientation of the head in 3D. Classical theories of the head-direction (HD) system in 2D rely on continuous attractor neural networks, where neurons with similar heading preference excite each other, while inhibiting other HD neurons. Local excitation and long-range inhibition promote the formation of a stable “bump” of activity that maintains a representation of heading. The extension of HD models to 3D is hindered by complications (i) 3D rotations are non-commutative (ii) the space described by all possible rotations of an object has a non-trivial topology. This topology is not captured by standard parametrizations such as Euler angles (e.g. yaw, pitch, roll). For instance, with these parametrizations, a small change of the orientation of the head could result in a dramatic change of neural representation. We used methods from the representation theory of groups to develop neural network models that exhibit patterns of persistent activity of neurons mapped continuously to the group of 3D rotations. I will further discuss how these networks can (i) integrate vestibular inputs to update the representation of heading, and (ii) be used to interpret “mental rotation” experiments in humans.
This is joint work with Hervé Rouault (CENTURI) and Alon Rubin (Weizmann Institute of Science).

10:30 – 11:00am
Coffee Break

11:00 – 11:45am
Sam Gershman
Title: The hippocampus as a predictive map
Abstract: A cognitive map has long been the dominant metaphor for hippocampal function, embracing the idea that place cells encode a geometric representation of space. However, evidence for predictive coding, reward sensitivity and policy dependence in place cells suggests that the representation is not purely spatial. I approach this puzzle from a reinforcement learning perspective: what kind of spatial representation is most useful for maximizing future reward? I show that the answer takes the form of a predictive representation. This representation captures many aspects of place cell responses that fall outside the traditional view of a cognitive map. Furthermore, I argue that entorhinal grid cells encode a low-dimensionality basis set for the predictive representation, useful for suppressing noise in predictions and extracting multiscale structure for hierarchical planning.

11:45 – 12:30pm
Lucia Jacobs
Title: The adaptive geometry of a chemosensor: the origin and function of the vertebrate nose
Abstract: A defining feature of a living organism, from prokaryotes to plants and animals, is the ability to orient to chemicals. The distribution of chemicals, whether in water, air or on land, is used by organisms to locate and exploit spatially distributed resources, such as nutrients and reproductive partners. In animals, the evolution of a nervous system coincided with the evolution of paired chemosensors. In contemporary insects, crustaceans, mollusks and vertebrates, including humans, paired chemosensors confer a stereo olfaction advantage on the animal’s ability to orient in space. Among vertebrates, however, this function faced a new challenge with the invasion of land. Locomotion on land created a new conflict between respiration and spatial olfaction in vertebrates. The need to resolve this conflict could explain the current diversity of vertebrate nose geometries, which could have arisen due to species differences in the demand for stereo olfaction. I will examine this idea in more detail in the order Primates, focusing on Old World primates, in particular, the evolution of an external nose in the genus Homo.

12:30 – 1:30pm
Lunch

1:30 – 2:15pm
Talia Konkle
Title: The shape of things and the organization of object-selective cortex
Abstract: When we look at the world, we effortlessly recognize the objects around us and can bring to mind a wealth of knowledge about their properties. In part 1, I’ll present evidence that neural responses to objects are organized by high-level dimensions of animacy and size, but with underlying neural tuning to mid-level shape features. In part 2, I’ll present evidence that representational structure across much of the visual system has the requisite structure to predict visual behavior. Together, these projects suggest that there is a ubiquitous “shape space” mapped across all of occipitotemporal cortex that underlies our visual object processing capacities. Based on these findings, I’ll speculate that the large-scale spatial topography of these neural responses is critical for pulling explicit content out of a representational geometry.

2:15 – 3:00pm
Vijay Balasubramanian
Title: Becoming what you smell: adaptive sensing in the olfactory system
Abstract: I will argue that the circuit architecture of the early olfactory system provides an adaptive, efficient mechanism for compressing the vast space of odor mixtures into the responses of a small number of sensors. In this view, the olfactory sensory repertoire employs a disordered code to compress a high dimensional olfactory space into a low dimensional receptor response space while preserving distance relations between odors. The resulting representation is dynamically adapted to efficiently encode the changing environment of volatile molecules. I will show that this adaptive combinatorial code can be efficiently decoded by systematically eliminating candidate odorants that bind to silent receptors. The resulting algorithm for “estimation by elimination” can be implemented by a neural network that is remarkably similar to the early olfactory pathway in the brain. The theory predicts a relation between the diversity of olfactory receptors and the sparsity of their responses that matches animals from flies to humans. It also predicts specific deficits in olfactory behavior that should result from optogenetic manipulation of the olfactory bulb.

3:00 – 3:45pm
Ila Feite
Title: Invariance, stability, geometry, and flexibility in spatial navigation circuits
Abstract: I will describe how the geometric invariances or symmetries of the external world are reflected in the symmetries of neural circuits that represent it, using the example of the brain’s networks for spatial navigation. I will discuss how these symmetries enable spatial memory, evidence integration, and robust representation. At the same time, I will discuss how these seemingly rigid circuits with their inscribed symmetries can be harnessed to represent a range of spatial and non-spatial cognitive variables with high flexibility.

3:45 – 4:00pm
L Mahadevan – summary

4/15/2019 Mathematical Physics Seminar
2019-04-15 12:00 - 13:00 | MA

4/17/2019 Fluid Dynamics Seminar
2019-04-17 15:00 | MA

Machine Learning Physics: From Quantum Mechanics to Holographic Geometry
2019-04-17 16:30 - 17:30 | MA
Speaker: Yi–Zhuang You (UCSD)

Title: Machine Learning Physics: From Quantum Mechanics to Holographic Geometry

Abstract: Inspired by the “third wave” of artificial intelligence (AI), machine learning has found rapid applications in various topics of physics research. Perhaps one of the most ambitious goals of machine learning physics is to develop novel approaches that ultimately allows AI to discover new concepts and governing equations of physics from experimental observations. In this talk, I will present our progress in applying machine learning technique to reveal the quantum wave function of Bose-Einstein condensate (BEC) and the holographic geometry of conformal field theories. In the first part, we apply machine translation to learn the mapping between potential and density profiles of BEC and show how the concept of quantum wave function can emerge in the latent space of the translator and how the Schrodinger equation is formulated as a recurrent neural network. In the second part, we design a generative model to learn the field theory configuration of the XY model and show how the machine can identify the holographic bulk degrees of freedom and use them to probe the emergent holographic geometry.

[1] C. Wang, H. Zhai, Y.-Z. You. Uncover the Black Box of Machine Learning Applied to Quantum Problem by an Introspective Learning Architecture https://arxiv.org/abs/1901.11103
[2] H.-Y. Hu, S.-H. Li, L. Wang, Y.-Z. You. Machine Learning Holographic Mapping by Neural Network Renormalization Group https://arxiv.org/abs/1903.00804
[3] Y.-Z. You, Z. Yang, X.-L. Qi. Machine Learning Spatial Geometry from Entanglement Features https://arxiv.org/abs/1709.01223

Yip Annual Lecture
2019-04-18 16:00 - 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On April 18, 2019 Harvard CMSA hosted the inaugural Yip lecture. The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip. This year’s speaker was Peter Galison (Harvard Physics).
The lecture was held from 4:00-5:00pm in Science Center, Hall A.

4/18/2019 General Relativity Seminar
2019-04-19 09:30 - 10:30 | MA

4/22/2019 Quantum Matter Seminar
2019-04-22 10:30 - 12:00 | MA

4/22/2019 Math Physics Seminar
2019-04-22 12:00 - 13:00 | MA

4/24/2019 Topological Aspects of Condensed Matter Seminar
2019-04-24 10:30 - 12:00 | MA

4/24/2019 General Relativity Seminar
2019-04-24 10:30 - 23:30 | MA

4/24/2019 Fluid Dynamics Seminar
2019-04-24 15:00 - 16:00 | MA

Credible Mechanisms
2019-04-24 16:30 - 17:30 | MA
Speaker: Shengwu Li (Harvard)

Title: Credible Mechanisms

Abstract: Consider an extensive-form mechanism, run by an auctioneer who communicates sequentially and privately with agents. Suppose the auctioneer can deviate from the rules provided that no single agent detects the deviation. A mechanism is credible if it is incentive-compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first-price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy-proof mechanism.

4/25/2019 Fluid Dynamics Seminar
2019-04-25 00:00 - 13:00 | MA

4/25/2019 General Relativity Seminar
2019-04-25 10:30 - 23:30 | MA

4/26/2019 Topology
2019-04-26 10:30 - 12:40 | MA

4/26/2019 General Relativity Seminar
2019-04-26 14:30 - 2020-04-26 15:30 | MA

Conference on Algebraic Geometry, Representation theory and Mathematical Physics
2019-04-29 09:00 - 2019-05-01 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
From April 29 to May 1, 2019 the CMSA will be hosting a Conference on Algebraic Geometry, Representation theory and Mathematical Physics. This workshop is organized by Bong Lian (Brandeis) and Artan Sheshmani (CMSA) . The workshop will be held in room G10 of the CMSA, located at 20 Garden Street, Cambridge, MA.
Videos
Speakers:

Dan Abramovich, Brown
Roman Bezrukavnikov, MIT
Fedor Bogomolov, NYU
Qile Chen, Boston College
Dawei Chen, Boston College
Alexander Efimov, Moscow
Pavel Etingof, MIT
Maksym Fedorchuk, Boston College
Dennis Gaitsgory, Harvard
Amin Gholampour, Maryland
Brendan Hassett, Brown
Ludmil Katzarkov, Miami & Moscow
Si Li, Tsinghua
Andrei Negut, MIT
Yuri Tschinkel, NYU
Wei Zhang, MIT

Monday, April 29

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 10:00am
Wei Zhang, MIT
Title: The arithmetic fundamental lemma for diagonal cycles
Abstract: I’ll recall the Gross–Zagier theorem and a high dimensional generalization, the arithmetic Gan-Gross-Prasad conjecture, which relates the height pairing of arithmetic diagonal cycles on certain shimura varieties to the first order derivative of certain L-functions. The arithmetic fundamental lemma conjecture arises from the relative trace formula approach to this conjecture. I will recall the statement of the arithmetic fundamental lemma and outline a proof.

10:00 – 10:30am
Break

10:30 – 11:30am
Yuri Tschinkel, NYU
Title: Equivariant birational geometry and modular symbols
Abstract: We introduce new invariants in equivariant birational geometry and study their relation to modular symbols and cohomology of arithmetic groups (joint with M. Kontsevich and V. Pestun).

11:30 – 1:30pm
Lunch

1:30 – 2:30pm
Alexander Efimov, Moscow
Title: Torsionness for regulators of canonical extensions
Abstract: I will sketch a generalization of the results of Iyer and Simpson arXiv:0707.0372 to the general case of a normal-crossings divisor at infinity.

2:30 – 3:00pm
Break

3:00 – 4:00pm
Amin Gholampour, Maryland
Title: Euler Characteristics of punctual quot schemes on threefolds
Abstract: Let F be a homological dimension 1 torsion free sheaf on a nonsingular quasi-projective threefold. The first cohomology of the derived dual of F is a 1-dimension sheaf G supported on the singular locus of F. We prove a wall-crossing formula relating the generating series of the Euler characteristics of Quot(F, n) and Quot(G,n), where Quot(-,n) denotes the quot scheme of length n quotients. We will use this relation in studying the Euler characteristics of the moduli spaces of stable torsion free sheaves on nonsingular projective threefolds. This is a joint work with Martijn Kool.

4:00 – 4:30pm
Break

4:30 – 5:30pm
Maksym Fedorchuck, BC
Title: Stability of one-parameter families of weighted hypersurfaces
Abstract: We define a notion of stability for fibrations over a curve with generic fibers being weighted hypersurfaces (in some weighted projective space) generalizing Kollár’s stability for families of hypersurfaces in a projective space. The stability depends on a choice of an effective line bundle on the parameter space of weighted hypersurfaces and different choices pick out different birational model of the total space of the fibration. I will describe enumerative geometry that goes into understanding these stability conditions, and, if time permits, examples where this machinery can be used to produce birational models with good properties. Joint work with Hamid Ahmadinezhad and Igor Krylov.

Tuesday, April 30

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 10:00am
Brendan Hassett, Brown
Title: Rationality for geometrically rational threefolds
Abstract: We consider rationality questions for varieties over non-closed fields that become rational over an algebraic closure, like smooth complete intersections of two quadrics. (joint with Tschinkel)

10:00 – 10:30am
Break

10:30 – 11:30am
Dennis Gaitsgory, Harvard
Title: The Fundamental Local Equivalence in quantum geometric Langlands
Abstract: The Fundamental Local Equivalence is statement that relates the q-twisted Whittaker category of the affine Grassmannian for the group G and the category of modules over the Langlands dual “big” quantum group. The non-triviaiity of the statement lies is the fact that the relationship between the group and its dual is combinatorial, so to prove the FLE one needs to express both sides in combinatorial terms. In the talk we will indicate the proof of a related statement for the “small” quantum group. The combinatorial link is provided by the category of factorization modules over a certain factorization algebra, which in itself is a geometric device that concisely encodes the root data.

11:30 – 1:00pm
Lunch

1:00- 2:00pm
Andrei Negut, MIT
Title: AGT relations in geometric representation theory
Abstract: I will survey a program that seeks to translate the Alday-Gaiotto-Tachikawa correspondence (between gauge theory on R^4 and conformal field theory) into the language of algebraic geometry. The objects of study become moduli spaces of sheaves on surfaces, and the goal is to connect them with the W-algebra of type gl_n.

2:00 – 2:15pm
Break

2:15 – 3:15pm
Dan Abramovich, Brown
Title: Resolution in characteristic 0 using weighted blowing up
Abstract: Given a variety $X$, one wants to blow up the worst singular locus, show that it gets better, and iterate until the singularities are resolved.
Examples such as the whitney umbrella show that this iterative process cannot be done by blowing up smooth loci – it goes into a loop.
We show that there is a functorial way to resolve varieties using emph{weighted} blowings up, in the stack-theoretic sense. To an embedded variety $X subset Y$ one functorially assigns an invariant $(a_1,ldots,a_k)$, and a center locally of the form $(x_1^{a_1} , ldots , x_k^{a_k})$, whose stack-theoretic weighted blowing up has strictly smaller invariant under the lexicographic order.
This is joint work with Michael Tëmkin (Jerusalem) and Jaroslaw Wlodarczyk (Purdue), a side product of our work on functorial semistable reduction. A similar result was discovered by G. Marzo and M. McQuillan.

3:15 – 3:30pm
Break

3:30 – 4:30pm
Fedor Bogomolov, NYU
Title: On the base of a Lagrangian fibration for a compact hyperkahler manifold.
Abstract: In my talk I will discuss our proof with N. Kurnosov that the base of such fibration for complex projective manifold hyperkahler manifold of dimension $4$ is always a projective plane $P^2$. In fact we show that the base of such fibration can not have a singular point of type $E_8$. It was by the theorem of Matsushita and others that only quotient singularities can occur and if the base is smooth then the it is isomorphic to $P^2$. The absence of other singularities apart from $E_8$ has been already known and we show that $E-8$ can not occur either. Our method can be applied to other types of singularities for the study of Lagrangian fibrations in higher dimensions More recently similar result was obtained by Huybrechts and Xu.

4:30 – 4:45pm
Break

4:45 – 5:45pm
Dawei Chen, BC
Title: Volumes and intersection theory on moduli spaces of Abelian differentials
Abstract: Computing volumes of moduli spaces has significance in many fields. For instance, Witten’s conjecture regarding intersection numbers on moduli spaces of Riemann surfaces has a fascinating connection to the Weil-Petersson volume, which motivated Mirzakhani to give a proof via Teichmueller theory, hyperbolic geometry, and symplectic geometry. In this talk I will introduce an analogue of Witten’s intersection numbers on moduli spaces of Abelian differentials to compute the Masur-Veech volumes induced by the flat metric associated with Abelian differentials. This is joint work with Moeller, Sauvaget, and Zagier (arXiv:1901.01785).

Wednesday, May 1

Time
Speaker
Title/Abstract

8:30 – 9:00am
Breakfast

9:00 – 10:00am
Pavel Etingof, MIT
Title: Short star-products for filtered quantizations
This is joint work with Eric Rains and Douglas Stryker.

10:00 – 10:30am
Break

10:30 – 11:30am
Roman Bezrukavnikov, MIT
Title: Stability conditions and representation theory
Abstract: I will recall the concept of real variation of stabilities (introduced in my work with Anno and Mirkovic)
and its relation to modular Lie algebra representations. I will also address a potential generalization of that picture
to modular representations of affine Lie algebras related to the classical limit of geometric Langlands duality and its local counterpart.

11:30 – 11:45am
Break

11:45 – 12:45pm
Qile Chen, BC
Title: Counting curves in critical locus via logarithmic compactification
Abstract: An R-map consists of a pre-stable map to possibly non-GIT quotient together with sections of certain spin bundles. The moduli of R-maps are in general non-compact. When the target of R-maps is equipped with a super-potential W with compact critical locus, using Kiem-Li cosection localization it has been proved by many authors in various settings that the virtual cycle of R-maps can be represented by the cosection localized virtual cycle which is supported on the proper locus consisting of R-maps in the critical locus of W. Though the moduli of R-maps is equipped with a natural torus action by scaling of the spin bundles, the non-compactness of the R-maps moduli makes such powerful torus action useless.
In this talk, I will introduce a logarithmic compactification of the moduli of R-maps using certain modifications of stable logarithmic maps. The logarithmic moduli space carries a canonical virtual cycle from the logarithmic deformation theory. In the presence of a super-potential with compact critical locus, it further carries a reduced virtual cycle. We prove that (1) the reduced virtual cycle of the compactification can be represented by the cosection localized virtual cycle; and (2) the difference of the canonical and reduced virtual cycles is another reduced virtual cycle supported along the logarithmic boundary. As an application, one recovers the Gromov-Witten invariants of the critical locus as the invariants of logarithmic R-maps of its ambient space in an explicit form. The latter can be calculated using the spin torus action.
This is a joint work with Felix Janda and Yongbin Ruan.

12:45 – 2:30pm
Lunch

2:30 – 3:30pm
Si Li, Tsinghua
Title: Semi-infinite Hodge structure: from BCOV theory to Seiberg-Witten geometry
Abstract: I will explain how the semi-infinite Hodge theory extends Kodaira-Spencer gravity (Bershadsky-Cecotti-Ooguri-Vafa theory of B-twisted closed topological string field theory) into a full solution of Batalin-Vilkovisky master equation. This allows us to formulate quantum B-model via a rigorous BV quantization method and construct integrable hierarchies arising naturally from the background symmetry. In the second part of the talk, I will explain the recent discovery of the connection between K.Saito’s primitive form and 4d N=2 Seiberg-Witten geometry arising from singularity theory.

3:30 – 4:00pm
Break

4:00 – 5:00pm
Ludmil Katzarkov, Moscow
Title: PDE’s non commutative motives and HMS.
Abstract: In this talk we will discuss the theory of central manifolds and the new structures in geometry it produces. Application to Bir. Geometry will be discussed.

4/29/2019 Quantum Matter seminar
2019-04-29 10:30 - 12:00 | MA

4/29/2019 Mathematical Physics Seminar
2019-04-29 12:00 - 13:00 | MA

5/1/2019 Fluid Dynamics Seminar
2019-05-01 15:00 - 16:00 | MA

Conference on Differential Geometry, Calabi-Yau theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau
2019-05-02 09:00 - 2019-05-05 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
On May 2-5, 2019 the Harvard Mathematics Department hosted a Conference on Differential Geometry, Calabi-Yau Theory and General Relativity: A conference in honor of the 70th Birthday of Shing-Tung Yau. The conference was held in the Science Center, Lecture Hall C.
Organizers:

Horng-Tzer Yau (Harvard)
Wilfried Schmid (Harvard)
Clifford Taubes (Harvard)
Cumrun Vafa (Harvard)

Speakers:

Lydia Bieri, University of Michigan
Tristan Collins, MIT
Simon Donaldson, Imperial College
Fan Chung Graham, UC San Diego
Nigel Hitchin, Oxford University
Jun Li, Stanford University
Kefeng Liu, UCLA
Chiu-Chu Melissa Liu, Columbia University
Alina Marian, Northeastern University
Xenia de la Ossa, Oxford University
Duong H. Phong, Columbia University
Richard Schoen, UC Irvine
Andrew Strominger, Harvard University
Nike Sun, MIT
Clifford Taubes, Harvard University
Chuu-Lian Terng, UC Irvine
Valentino Tosatti, Northwestern University
Karen Uhlenbeck, University of Texas
Cumrun Vafa, Harvard University
Mu Tao Wang, Columbia University
Edward Witten, IAS
Stephen Yau, Tsinghua University, P.R. China

5/6/2019 Math Physics
2019-05-06 12:00 - 13:00 | MA
