5,459 Works

Tutorial: Agent-Based Modeling

Christina Mair
FRED tutorial by Mary Krauland and Dave Galloway

Monopoles and difference modules

Takuro Mochizuki
We shall discuss equivalences between various types of monopoles and difference modules. They are variants of Kobayashi-Hitchin correspondences between algebro-geometric objects and differential geometric objects. We may also regard them as equivalences between monopoles and their underlying scattering data, which have been pursued in various contexts. Though it is difficult to construct monopoles explicitly, we would like to explain that some asymptotic properties can be easily understood through the corresponding difference modules.

Uniform spanning trees in high dimension 3

Tom Hutchcroft
<p>Uniform spanning trees have played an important role in modern probability theory as a non-trivial statistical mechanics model that is much more tractable than other (more physically relevant) models such as percolation and the Ising model. It also enjoys many connections with other topics in probability and beyond, including electrical networks, loop-erased random walk, dimers, sandpiles, l^2 Betti numbers, and so on. In this course, I will introduce the model and explain how we can...

Deep Reading, Critical Thinking, and Empathy in the Age of COVID : A Digital Dilemma

Maryanne Wolf
Dr. Wolf has dedicated her professional career to children with learning challenges. Her research focuses on dyslexia, literacy in digital culture, and the reading brain circuit. She designed the RAVE-O reading intervention for children with dyslexia. Dr. Wolf is the author of Proust and the Squid (2007), translated into 13 languages, Tales of Literacy for the 21st Century (2016), and Reader, Come Home: The Reading Brain in a Digital World (2018). She has been the...

The Cultural and Natural Legacy in the Cradle of Maya Civilization : The Mirador-Calakmul Basin of Guatemala and Mexico

Richard D. Hansen
Dr. Hansen has identified some of the largest and earliest ancient cities of the Mayan civilization in Central America with a major international archaeological research team with scholars from around the globe. His work has been featured in 36 film documentaries and he was the principal consultant for the movie Apocalypto (Mel Gibson), CBS’s Survivor Guatemala, and National Geographic’s The Story of God with Morgan Freeman. In 2013, he was named as “one of 24...

Tracking the structural diversity of carbapenemase-producing plasmids using single molecule sequencing.

Nicholas Noll
The rapid global increase of multidrug-resistant organisms presents a major global health threat that will dramatically reduce the efficacy of antibiotics and thus constrain the number of effective treatments available to patients. As opposed to analogous efforts in viral epidemiology, accurate reconstruction of the pandemic spread of antibiotic resistance remains intractable for reasonable sample sizes due, in large part, to the high rate of homologous recombination and horizontal gene transfer that prevents the application of...

Multistage Stochastic Capacity Planning Using JuDGE

Andy Philpott
Julia Dynamic Generation Expansion (JuDGE) is a Julia package for solving stochastic capacity expansion problems formulated in a "coarse-grained" scenario tree that models long-term uncertainties. The user provides JuDGE with a coarse-grained tree and a JuMP formulation of a stage problem to be solved in each node of this tree. JuDGE then applies Dantzig-Wolfe decomposition to this framework based on the general model of Singh et al. (2009). The stage problems are themselves single-stage capacity...

Constructions of high dimensional caps, sets without arithmetic progressions, and sets without zero sums

Christian Elsholtz
In this talk we discuss the following problems. \begin{enumerate} \item For a finite abelian group $G$ let $\mathsf s (G)$ denote the smallest integer $l$ such that every sequence $S$ over $G$ of length $|S| \ge l$ has a zero-sum subsequence of length $\exp (G)$. Specialising to $G=\mathbb{Z}_n^r$, the Erd\H{o}s-Ginzburg-Ziv theorem states that $\mathsf s (\mathbb{Z}_n)=2n-1$ and Reiher proved that $\mathsf s (\mathbb{Z}_n^2)=4n-3$. The speaker proved (some years ago) that for odd $n$ $\mathsf s...

From representations of p-adic groups to congruences of automorphic forms

Jessica Fintzen
I will present new results about the representation theory of $p$-adic groups and demonstrate how these can be used to obtain congruences between arbitrary automorphic forms and automorphic forms which are supercuspidal at $p$. This simplifies earlier constructions of attaching Galois representations to automorphic representations for general linear groups (and general unitary groups). Moreover, our results apply to general reductive groups and have therefore the potential to become widely applicable beyond the case of the...

Physical constraints on epistasis in proteins and gene regulatory networks

Arvind Murugan
Living systems evolve one mutation at a time, but a single mutation can alter the effect of subsequent mutations. The underlying mechanistic determinants of such epistasis are unclear. Here, we argue that the physical properties of a biological system can generically and easily constrain its epistasis. We analyze the interaction between mutations in generic models of proteins and biochemical networks. In each case, a slow, collective physical mode is actuated upon mutation, reducing the dimensionality...

Open Problems in the Reverse Mathematics of Ramsey Theory on Trees and Graphs

Natasha Dobrinen

Large deviations for random networks and applications - 2

Shirshendu Ganguly
While large deviations theory for sums and other linear functions of independent random variables is well developed and classical, the set of tools to analyze non-linear functions, such as polynomials, is limited. Canonical examples of such non-linear functions include subgraph counts and spectral observables in random networks. In this series of lectures we will review the recent exciting developments around building a suitable nonlinear large deviations theory to treat such random variables and understand geometric...

Asymptotic properties of linear field equations in anti-de Sitter space

Jonathan Luk

Twisted affine Grassmannians over the integers

João Nuno Pereira Lourenço
Let $G$ be a quasi-split reductive connected group over $\mathbb{Q}(t)$ which splits over $\mathbb{Q}(\zeta_e, t^{1/e})$, $e=2$ or $3$, whose derived group is absolutely simple simply connected and whose maximal torus corresponds to a sum of permutation modules of rank 1 or $e$. Fixing a maximal split torus $S$ of $G$ and a facet $\mathbf{f}$ of the apartment corresponding to $S$ in the building of $G$ over $\mathbb{Q}((t))$, we construct a smooth, affine and connected group...

A hunt for new descriptions of old quasicrystals via soft-packing

Jean Taylor
Jean Taylor, currently at University of California, Berkeley. Marjorie and I are interested in how crystals grow, especially how quasicrystals grow. In the case of multi-element alloys, it is highly likely to be by formation and then aggregation of clusters. There are many reasons to suspect icosahedral order may be important in forming many clusters; periodicity or quasiperiodicity would then arise from how these local clusters aggregate. Overlapping rhombic triacontahedra (RTs) are central to describing...

On Bayesian Estimation for Join the Shortest Queue Model

Ehssan Ghashim
We are concerned with an M /M /- join the shortest queue model with N parallel queues for an arbitrary large N, in which each queue has a dedicated input stream. Each server has an exponential service rate μ. Assuming the steady-state case, a bayesian paradigm is used in estimating the traffic intensity based on queue length data only and based on the mean field interaction model for the limiting behavior of the JSQ model...

Queueing and Markov chain decomposition method to analyze Markov-modulated Markov chains

Katsunobu Sasanuma
We present a Queueing and Markov chain decomposition method based on the total expectation theorem. Our decomposition method requires partial flow to be conserved, which we call a termination scheme. This scheme is useful when deriving analytical formulas for complex queueing systems. As an example, we apply our method to derive an exact set of stationary equations for the probability generating functions of decomposed chains of Markov-modulated continuous-time Markov chains.

Rational torsion points on J_0(N)

Hwajong Yoo
For any positive integer N, we propose a conjecture on the rational torsion points on J_0(N). Also, we prove this conjecture up to finitely many primes. More precisely, we prove that the prime-to-m parts of the rational torsion subgroup of J_0(N) and the rational cuspidal divisor class group of X_0(N) coincide, where m is the largest perfect square dividing 12N.

Principal polarizations and Shimura data for families of cyclic covers of the projective line

Rachel Pries
Consider a family of degree m cyclic covers of the projective line, with any number of branch points and inertia type. The Jacobians of the curves in this family are abelian varieties having an automorphism of order m with a prescribed signature. For each such family, the signature determines a PEL-type Shimura variety. Under a condition on the class number of m, we determine the Hermitian form and Shimura datum of the component of the...

Modularity of elliptic curves over totally real quartic fields not containing the square root of 5

Josha Box
Following Wiles's breakthrough work, it has been shown in recent years that elliptic curves over each totally real field of degree 2 (Freitas-Le Hung-Siksek) or 3 (Derickx-Najman-Siksek) are modular. We study the degree 4 case and show that if K is a totally real quartic field in which 5 is not a square, then every elliptic curve over K is modular. Thanks to strong results of Thorne and Kalyanswami, this boils down to the determination...

A Chabauty-Coleman bound for surfaces in abelian threefolds

Hector Pasten
We will give a bound for the number of rational points in a hyperbolic surface contained in an abelian threefold of Mordell-Weil rank $1$ over $\mathbb{Q}$. The form of the estimate is analogous to the classical Chabauty-Coleman bound for curves, although the proof uses a completely different approach. The new method concerns w-integral schemes, especially in positive characteristic. This is joint work with Jerson Caro.

Hasse principle for a family of K3 surfaces

Daniel Loughran
In this talk we study the Hasse principle for the family of "diagonal K3 surfaces of degree 2", given by the explicit equations: $$w^2 = A_1 x_1^6 + A_2 x_2^6 + A_3 x_3^6.$$ I will explain how many such surfaces, when ordered by their coefficients, have a Brauer-Manin obstruction to the Hasse principle. This is joint work with Damián Gvirtz and Masahiro Nakahara.

Mean field methods in high-dimensional statistics and nonconvex optimization - 2

Andrea Montanari
Starting in the seventies, physicists have introduced a class of random energy functions and corresponding random probability distributions (Gibbs measures), that are known as mean-field spin glasses. Over the years, it has become increasingly clear that a broad array of canonical models in random combinatorics and (more recently) high-dimensional statistics are in fact examples of mean field spin glasses, and can be studied using tools developed in that area. Crucially, these new application domains have...

Categorification and geometric group theory

Anthony Licata
One of the upshots of categorification constructions in representation theory is a nice stock of examples of actions of groups (e.g. braid groups) on triangulated categories. The goal of this talk will be to explain how, following an analogy with the study of mapping class groups of surfaces via Teichmuller theory, such categorical constructions can be used to study the groups themselves.

Sparse Multiscale with Phase to model Deep Neural Networks

Stephane Mallat

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