This Week at ICERM
Your device timezone is . Do you want to view schedules in or choose a custom timezone?
September 24, 2023
There are no events currently scheduled for September 24th.
September 25, 2023

10:00  11:00 am EDTJournal Club11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space

3:30  5:00 pm EDTTLN Working GroupGroup Work  10th Floor Classroom
September 26, 2023

9:00  10:30 am EDTTutorialTutorial  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
September 27, 2023

9:00  10:00 am EDTProfessional Development: Ethics IProfessional Development  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
September 28, 2023

9:00  10:30 am EDTTutorialTutorial  11th Floor Lecture Hall

12:00  1:30 pm EDTOpen Problems Lunch SeminarWorking Lunch  11th Floor Lecture Hall

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
September 29, 2023

8:30  8:50 am EDTCheck In11th Floor Collaborative Space

8:50  9:00 am EDTWelcome11th Floor Lecture Hall
 Brendan Hassett, ICERM/Brown University

9:00  9:45 am EDTFormulas for Macdonald polynomials via the multispecies exclusion and zero range processes11th Floor Lecture Hall
 Olya Mandelshtam, University of Waterloo
Abstract
We describe some recently discovered connections between onedimensional interacting particle models and Macdonald polynomials and show the combinatorial objects that make this connection explicit. The first such model is the multispecies asymmetric simple exclusion process (ASEP) on a ring, linked to the symmetric Macdonald polynomials P_\lambda through its partition function, with multiline queues as the corresponding combinatorial object. The second particle model is the multispecies totally asymmetric zero range process (TAZRP) on a ring, which was recently found to have an analogous connection to the modified Macdonald polynomial H_\lambda. The combinatorial objects interpolating between probabilities of the TAZRP and the modified Macdonald polynomials turn out to be tableaux with a queue inversion statistic. We explain the plethystic relationship between multiline queues and queue inversion tableaux, and along the way, derive a new formula for P_\lambda using the queue inversion statistic. This plethystic correspondence is closely related to fusion in the setting of integrable systems.

10:00  10:30 am EDTCoffee Break11th Floor Collaborative Space

10:30  11:15 am EDTDimers in 3D11th Floor Lecture Hall
 Catherine Wolfram, MIT
Abstract
A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. Given a compact region R in R^d, consider regions R_n in (1/n) Z^d which approximate R (and some boundary condition). What do random dimer tilings of R_n look like for large n? The 2D version of this question was answered by Cohn, Kenyon, and Propp in 2000. I will talk about how to answer this question in 3D. In both cases, it turns out that a random tiling of R_n is exponentially more likely to lie close to a fixed ""limit shape"" (and more generally, there is a large deviation principle, meaning the probability of lying close to any possible limiting configuration is given by a function called the ""rate function""). While the results are analogous, I will explain that the methods of proof are very different, because many of the key tools for studying dimers are special to two dimensions. This talk is based on https://arxiv.org/abs/2304.08468, which is joint work with Nishant Chandgotia and Scott Sheffield.

11:30 am  12:15 pm EDTDimer models and local systems11th Floor Lecture Hall
 Haolin Shi, Yale University
Abstract
The dimer model studies a natural probability measure on the space of perfect matching (""dimer covers"") of an edgeweighted graph; the probability of a dimer cover is proportional to the product of its edge weights. When the graph is bipartite, a useful change in viewpoint is to view the edge weights as defining a ""C∗ local system"", that is a line bundle with connection. This leads us to consider natural generalizations using higherrank bundles, in particular SLn local systems. We will talk about a collection of results with emphasis on calculating connection probabilities in double and triple dimer models.

12:25  12:30 pm EDTGroup Photo (Immediately After Talk)11th Floor Lecture Hall

12:30  2:30 pm EDTLunch/Free Time

2:30  3:15 pm EDTDiagram algebras11th Floor Lecture Hall
 Rosa Orellana, Dartmouth College
Abstract
One of the bestknown planar diagram algebras is the TemperleyLieb algebra. This algebra is defined combinatorially using nonintersecting matchings and can be realized as a centralizer of Lie algebras (or quantum groups) acting on tensor space. They have a wide range of applications, most notably to knot theory and statistical mechanics. The partition algebra is a generalization of the TemperleyLieb algebra which was proposed by Martin to study higher dimensional statistical models. In this talk I will discuss planar subalgebras of the partition algebras related to the TemperleyLieb algebra. This is joint work with N. Wallace and M. Zabrocki.

3:30  4:00 pm EDTCoffee Break11th Floor Collaborative Space

4:00  4:45 pm EDTRestricted permutations11th Floor Lecture Hall
 Richard Kenyon, Yale University
Abstract
We discuss large permutations with restricted permutation matrices, that is, whose permutation matrix has no 1s in some region. We give enumerative results and limit shapes.

5:00  6:30 pm EDTReception11th Floor Collaborative Space

11:00  11:30 am EDTRecurrent network models for predictive processingPost Doc/Graduate Student Seminar  10th Floor Classroom
 Bin Wang, University of California, San Diego
Abstract
Predictive responses to sensory stimuli are prevalent across cortical networks and are thought to be important for multisensory and sensorimotor learning. It has been hypothesized that predictive processing relies on computations done by two separate functional classes of cortical neurons: one specialized for “faithful” representation of external stimuli, and another for conveying predictionerror signals. It remains unclear how such predictive representations are formed in natural conditions, where stimuli are highdimensional. In this presentation, I will present some efforts on characterizing how highdimensional predictive processing can be performed through recurrent networks. I will start with the neuroscience motivations, define the mathematical models and mention some related mathematical questions that we haven't yet solved along the way.

11:30 am  12:00 pm EDTFishing for beta: uncovering mechanisms underlying cortical oscillations in largescale biophysical modelsPost Doc/Graduate Student Seminar  10th Floor Classroom
 Nicholas Tolley, Brown University
Abstract
Beta frequency (1330 Hz) oscillations are robustly observed across the neocortex, and are strongly predictive of behavior and disease states. While several theories exist regarding their functional significance, the cell and circuit level activity patterns underlying the generation of beta activity remains uncertain. We approach this problem using the Human Neocortical Neurosolver (HNN; hnn.brown.edu), a detailed biophysical model of a cortical column which simulates the microscale activity patterns underlying macroscale field potentials like beta oscillations. Detailed biophysical models potentially offer concrete and biologically interpretable predictions, but their use is challenged by computationally expensive simulations, an overwhelmingly large parameter space, and highly complex relationships between parameters and model outputs. We demonstrate how these challenges can be overcome by combining HNN with simulation based inference (SBI), a deep learning based Bayesian inference framework, and use it to characterize the space of parameters capable of producing beta oscillations. Specifically, we use the HNNSBI framework to characterize the constraints on network connectivity for producing spontaneous beta. In future work, we plan to compare these predictions to higher level neural models to identify which simplifying assumptions are consistent with detailed models of neural oscillations.

1:30  3:00 pm EDTTopology+Neuro Working GroupGroup Work  10th Floor Classroom

3:00  3:30 pm EDTCoffee Break11th Floor Collaborative Space
September 30, 2023

8:30  9:15 am EDTA Sanovtype theorem for Unimodular Marked Random Graphs, and its applications11th Floor Lecture Hall
 Kavita Ramanan, Brown University
Abstract
We establish a large deviation principle in a strong topology for the component empirical measure of several sequences of marked random graph models, including ErdosRenyi random graphs, random regular graphs, and more general configuration models. We show that the corresponding rate function is given by a relatively tractable formula involving the relative entropy functional. We also describe several applications of this result, such as Gibbs conditioning principles. This talk is based on joint work with IHsun Chen and Sarath Yasodharan.

9:30  10:15 am EDTPermutation limits (Permutons)11th Floor Lecture Hall
 Sumit Mukherjee, Columbia University
Abstract
Permutation limit theory arises by viewing a permutation as a probability measure on the unit square, and is motivated by dense graph limit theory. Using the theory of permutation limits (permutons), we can compute limiting properties of various permutation statistics for random permutations, such as number of fixed points, number of small cycles, pattern counts, and degree distribution of permutation graphs. We can also derive LDPs for random permutations. Our results apply to many non uniform distributions on permutations, including the the celebrated Mallows model, and murandom permutations. This is based on joint work with Bhaswar Bhattacharya, Jacopo Borga, Sayan Das and Peter Winkler.

10:30  11:00 am EDTCoffee Break11th Floor Collaborative Space

11:00  11:45 am EDTHigherOrder Graphon and Permuton Theories: Fluctuations, Inference, and Degeneracies11th Floor Lecture Hall
 Bhaswar Bhattacharya, University of Pennsylvania
Abstract
Motifs (patterns of subgraphs), such as edges and triangles, encode important structural information about the geometry of a network. Consequently, counting motifs in a large network is an important statistical and computational problem. In this talk we will consider the problem of estimating motif densities and fluctuations of subgraph counts in an inhomogeneous random graph sampled from a graphon. We will show that the limiting distributions of subgraph counts can be Gaussian or nonGaussian, depending on a notion of regularity of subgraphs with respect to the graphon. Using these results and a novel multiplier bootstrap for graphons, we will construct confidence intervals for the motif densities. We will also present parallel results for patterns in random permutations through the lens of permuton theory. Finally, we will discuss various structure theorems and open questions about degeneracies of the limiting distribution.

12:00  1:30 pm EDTLunch/Free Time

1:30  2:15 pm EDTInteractive workshop on planning a new active learning probability course for researchlevel students in mathadjacent fields.11th Floor Lecture Hall
 Robin Pemantle, University of Pennsylvania

2:30  3:00 pm EDTCoffee Break11th Floor Collaborative Space

3:00  4:00 pm EDT

4:00  5:00 pm EDTActive Learning Process11th Floor Lecture Hall
 Robin Pemantle, University of Pennsylvania
Abstract
The workshop will continue in an optional evening session, where we will make a plan for a course that fits the most populations of those attending the evening session. We will look over some existing materials, plan a shared materials archive, and discuss some of the more crucial mechanics of active classrooms.
All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC4).
All event times are listed in .
ICERM local time in Providence, RI is Eastern Daylight Time (UTC4). Would you like to switch back to ICERM time or choose a different custom timezone?
Schedule Timezone Updated