Hunter College Mathematics Colloquium

January 25

(Start of classes)

February 1

Rob Thompson (CUNY Hunter, Department of Mathematics and Statistics) Recording

Title: A report on the Mathematical Association of America’s studies on college calculus instruction and a summary of best practices

Abstract: The Mathematical Association of America conducted two extensive, NSF funded, studies of calculus instruction in American colleges and universities, the first of their kind. The first study took place from 2010-2015 and surveyed students and faculty from a large random sample of schools, collecting much data on who takes calculus, and how it is taught.  The study also included case studies from over 20 schools.   This study led to the formulation of seven “best practices”.

The second MAA study took place from 2015-2020 and involved a survey of all 330 graduate awarding mathematics departments in the US, along with case studies from around a dozen schools to examine the ways in which schools have implemented the seven best practices and to measure the effects of  changes made. 

In this talk I will report on some of the results from these studies.

February 8

Daniel Grange (SUNY Stony Brook, Department of Applied Mathematics) Recording

Title: Optimal Transport: Introduction and applications in filtering on Riemannian manifolds

Abstract: A few years before the French Revolution, Gaspard Monge introduced optimal transport, the problem of minimizing the average cost of transporting soil from the ground, deblais, to build fortifications, remblais. 150 years later Leonid Kantorovich characterized the problem in an economics setting, for which he later won the nobel prize. In this talk, I will discuss the evolution of the optimal transport problem, and how modern luminaries like Brenier and McCann, enable the computation of optimal transport maps on Riemannian manifolds for the use of sampling conditional probability distributions.

February 15

(Hiatus) 

February 22

(Monday schedule)

February 29

Kisung You (CUNY Baruch, Department of Mathematics) In-Person, HE 920

Title: Towards non-Euclidean space : an example of median

Abstract: A major trajectory in the development of statistics has been extending the scope of mathematical spaces behind the data we observe, from numbers to vectors, functions, and beyond. This has sparked both theoretical and computational breakthroughs. In this talk, I revisit the median, a robust alternative to the mean, as an example and introduce a novel extension of the concept in the space of probability measures under the framework of optimal transport. 

March 7

Ran Wei (Researcher at Verses AI) Recording

Title:  Developing resource-bounded adaptive agents with a single objective function

Abstract: Adaptive agents that can automate and augment human capabilities are of primary interest in current AI research. However, how to develop such agents in terms of choosing the appropriate decision variables, constraints, and objective functions has been an open question. Using the language of reinforcement learning and optimal control, I discuss a line of research aiming to develop resource-bounded agents with a single objective function and as a result eliminate catastrophes caused by training agent components on misaligned objectives. 

March 14

Silvia Ghinassi (University of Washington, Department of Mathematics) In-Person, HE 920

Title: Self-similar sets and Lipschitz graphs

Abstract: A one dimensional set is said to be purely unrectifiable if it has almost no shadows. In other words, if its intersection with any Lipschitz graph has measure zero. At what dimension do purely unrectifiable sets and Lipschitz graphs actually see each other? After a few preliminary answers, we will present the construction of Lipschitz graphs that intersect purely unrectifiable sets at high dimensions. We first take into account the special case of the four corner Cantor set and then generalize our construction for self similar sets, i.e. attractors of general iterated function systems satisfying a certain separation condition. I will include plenty of pictures and try to keep the talk accessible to a general audience of mathematicians. This is ongoing joint work with Blair Davey and Bobby Wilson.

Recording of a similar talk (missing intro).

Recording of a similar talk targeting experts.

Recording of short recording on the Analyst's Traveling Salesperson Theorem. 

Recording of an informal introduction to Geometric Measure Theory and Dimension.

March 21

(Hiatus)

March 28

Robert Ghrist (University of Pennsylvania, Department of Mathematics) In-person, Hemmerdinger Screening Room, HE 706

Title:  Opinion Dynamics on Sheaves

Abstract: There is a long history of networked dynamical systems that  models the spread of opinions over social networks, with the graph Laplacian playing a lead role.  One of the difficulties in modelling opinion dynamics is the presence of polarization: not everyone comes to consensus. This talk will describe work with Jakob Hansen introducing a new model for opinion dynamics using sheaves of vector spaces over social networks. The graph Laplacian is enriched to a Hodge Laplacian, and the resulting dynamics on discourse sheaves can lead to some very interesting and perhaps more realistic outcomes.  Extensions of these ideas will also be surveyed.

April 4

(Hiatus) 

April 11

(Hiatus) 

April 18

Jeremy Melvin (Open Block Labs) Recording

Title: A Mathematical Modeling Example: Sybil Detection in Crypto Protocols

Abstract: A sybil attack is where multiple entities, all operated by a single actor, masquerade as distinct individuals in order to exploit a system. These can be especially problematic for Crypto protocols attempting to provide rewards to their early users.  To combat this, using a combination of mathematical tools and machine learning methods, detection algorithms can be developed to cluster and classify entities.  First, I will provide some initial background on blockchains, decentralized apps and the airdrop mechanism.  Then, using the goal of sybil detection, I will go through the development process and the background and tools I rely on when approaching a problem as a data scientist/mathematical modeler.

April 25

(Spring break)

May 2

Speaker (Institution)

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May 9

Dorit Hammerling (Colorado School of Mines) In-Person, HE 920

Title: Quality Assurance for Earth System Models: a new statistical testing framework


Abstract: State-of-the-science climate models are valuable tools for understanding past and present climates and are particularly vital for addressing otherwise intractable questions about future climate scenarios.  The National Center for Atmospheric research leads the development of the popular Community Earth System Model (CESM), which models the Earth system by simulating the major Earth system components (e.g., atmosphere, ocean, land, river, ice, etc.) and the interactions between them.  These complex processes result in a model that is inherently chaotic, meaning that small perturbations can cause large effects.  For this reason, ensemble methods are common in climate studies, as a collection of simulations are needed to understand and characterize this uncertainty in the climate model system.  While climate scientists typically use initial condition perturbations to create ensemble spread, similar effects can result from seemingly minor changes to the hardware or software stack.  This sensitivity makes quality assurance challenging, and defining “correctness” separately from bit-reproducibility is really a practical necessity. Our approach casts correctness in terms of statistical distinguishability such that the problem becomes one of making decisions under uncertainty in a high-dimensional variable space.  We developed a statistical testing framework that can be thought of as hypothesis testing combined with Principal Component Analysis (PCA). One key advantage of this approach for settings with hundreds of output variables is that it not only captures changes in individual variables but the relationship between variables as well. This testing framework referred to as “Ensemble Consistency Testing” has been successfully implemented and used for the last few years, and we will provide an overview of this multi-year effort and highlight ongoing developments including a generalization to a broad class of numerical models with spatio-temporal output.

May 16

Speaker (Institution)

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