Interested in applying for graduate school, or debating doing so alongside some other career options? Symbols of Inclusion will be hosting a panel with the Math Club on October 2nd to answer any questions you may have about the process. Sitting on the panel, we’ll have two first years, a third year, and a fourth year graduate student. Another fourth year will moderate. In this way, we hope to be able to accurately address questions about the process itself from students who just went through it, as well as any questions that require more experience in graduate school itself. Please come armed with questions!

The K-moduli theory provides us with an approach to study moduli of curves. In this talk, I will introduce the K-moduli of certain log Fano pairs and how it relates to moduli of curves. We will see that the K-moduli spaces interpolate between different compactifications of moduli of curves. In particular, the K-moduli gives the last several Hassett-Keel models of moduli of curves of genus six.

The aim of this talk to show that several quantities as: the spectral radius of weakly irreducible tensors, spectral radius of uniform weighted hypergraphs, maximum of d-homogeneous polynomials with nonnegative coefficients in the unit ball of the d-Holder norm, are polynomially computable. This computability result is proven for a larger class of minimum of certain convex functions in R^n, which was considered by several authors. This is a joint work with Stephane Gaubert, INRIA and Centre de Mathematiques Appliquees (CMAP), Ecole polytechnique, IP Paris, France.

The HIGHWAVE project (2019-2025) is primarily on wave breaking. The major novelty during the first half of the project has been the experimental campaign with a smart boulder. The data, obtained by altering the breaking position of a wave impacting a vertical cliff, have demonstrated the influence of wave-impact mode (aerated, breaking or sloshing) on the displacement of clifftop boulders. This experimental campaign has shown the range of wave focusing positions most conducive to boulder movement and the range of displacement values we may expect in laboratory experiments. The absence of multiple repeated tests and the inability to fully quantify scaling effects mean that future work will firstly seek to reliably extrapolate these laboratory boulder displacement measurements to the real-world scale by quantifying pressure scaling errors using large scale tests, carrying out a larger number of repeated tests, and obtaining frictional similarity between prototype and laboratory scales. Additionally, a comparison between the importance of the wave-breaking position with the significant wave height and peak wave period should be carried out. At the beginning of the project we have been going back and forth between what one would like to measure to better understand wave breaking and what can be realistically measured in a hostile environment. The real potential impact of our results will be the degree to which they are able to describe real oceanic free surface profiles in a sea state where breaking occurs. However, although we have been able to access a range of data sets from wave buoys, ADCPs, radars, stereo vision, we have been surprised to note the lack of reliability of measurements of breaking wave events recorded in a given measurement time series or image as measurements hit technical recording limits or generate artifacts in the data. Indeed, we have come to realize that both the quality of the data and the sophistication of data analysis of existing wave measurements from sensors are based on decades-old technologies and methodologies and are unsatisfactory for the detailed study of breaking waves. Several theoretical results have been obtained as well: they range from new limiting configurations for surface waves to new links between superharmonic instability and wave breaking. Interesting results on wave forecasting and on the effect of rain on waves will also be presented. Acknowledgements: This work is funded by the European Research Council (ERC) under the EU Horizon 2020 research and innovation programme (grant agreement no. 833125-HIGHWAVE).

Dp-minimality is a kind of abstract model-theoretic "one-dimensionality" condition, satisfied for example by superstable theories of U-rank 1 and o-minimal theories. In this talk we will introduce dp-minimality, and then discuss some results on dp-minimal groups: namely, every torsion-free dp-minimal group is abelian, every stable dp-minimal group is solvable-by-finite, and every distal dp-minimal group is nilpotent-by-finite.

To any group G is associated the space Ch(G) of all characters on G. After defining this space and discussing its interesting properties, I'll turn to discuss dynamics on such spaces. Our main result is that the action of any arithmetic group on the character space of its amenable/solvable radical is stiff, i.e, any probability measure which is stationary under random walks must be invariant. This generalizes a classical theorem of Furstenberg for dynamics on tori. Relying on works of Bader, Boutonnet, Houdayer, and Peterson, this stiffness result is used to deduce dichotomy statements (and 'charmenability') for higher rank arithmetic groups pertaining to their normal subgroups, dynamical systems, representation theory and more. The talks is based on a joint work with Uri Bader.

A classical work of Linnik shows that the directions of primitive integer vectors on a "large" sphere are "equidistributed". I will discuss a joint work with Uri Shapira in which we consider an analogue of Linnik's problem inside the special linear group. The motivation behind our study is an extension of a previous work of Uri Shapira, Menny Aka and Manfred Einsiedler concerning the statistics of orthogonal grids of primitive integral vectors. I will present our results and a sketch of the main ideas in the proof – there’s a natural way to use the p-adics to generate integer points from a given integral point and to study those new points by looking on a certain periodic orbit in a homogeneous space.

This sentence is false; or is it? In this talk, I will motivate a rather provincial viewpoint in the philosophy of mathematics (using Gödel's first incompleteness theorem) which embraces the existence of paradoxes, and I will detail one mathematician's attempt to take this viewpoint seriously. In doing so, we will discuss Cantor's theorem in both classical and paraconsistent settings, we'll investigate relevant set theory, and we'll do a bit of inconsistent reasoning along the way.

TBA

Quantum mechanics allows quantum correlations – also called quantum entanglement – that are stronger than all the correlations we know from our daily lives. Their enigma has already troubled fathers of Quantum Mechanics. Einstein's ingenious skepticism about this theory gave rise to the fundamental philosophical question - formalized mathematically by John Bell - about the objective existence of properties of quantum particles before measurement. We shall discuss the related Bell inequalities tests from the perspective of randomness and stress that while quantum mechanical statistics look completely random, it may allow for a contribution of determinism, if we look at them from the perspective of possible future physical theories. This rises an interesting problem of certification of randomness and cryptographic security in hypothetical situations where eavesdropper has a post-quantum power. The two most natural post-quantum frameworks are the ones of no-signaling boxes and no- signaling assamblages. We discuss quantum correlations from the perspectives of the two frameworks. This includes on the one hand some no-go theorems and on the other hand some positive results concerning randomness amplification and generation of secure bits. [1] J. Barrett, L. Hardy, A. Kent, Phys. Rev. Lett. 95, 010503 (2005) [2] R. Renner. R. Collbeck, Nat. Phys. 8, 450 (2012) [3] F. G.S.L. Brandao, R. Ramanathan, A. Grudka, K. Horodecki, M. Horodecki, P. H., T. Szarek, H. Wojewodka, Nat. Comm. 7, 11345 (2016) [4] P. Horodecki and R. Ramanathan, Nat. Comm. 10,1701 (2019) [5] R. Ramanathan, M. Banacki, R. Ravel Rodrigues, P. Horodecki, npj Quantum Information, 8, 119 (2022). [6] M. Banacki, P. Mironowicz, R. Ramanathan, P. Horodecki, New J. Phys. 24, 083003 (2022) [7] A. B. Sainz, N. Brunner, D. Cavalcanti, P. Skrzypczyk, T. Vertesi, Phys. Rev. Lett. 115, 190403 (2015) [8] M. Banacki, R. Ramanathan, P. Horodecki, Multipartite channel assemblages, arXiv:2205.05033 (2022).

Church-Ellenberg-Farb and Miller-Wilson proved that for a nice enough manifold X and fixed k, the k-th homology group of the ordered configuration space of points in X stabilizes in a representation-theoretic sense as the number of points in the configuration space increases. By fixing a metric on X and replacing points with open unit-diameter disks, we get a new family of configuration spaces where the geometry of X comes to the forefront. One of the simplest of these disk configuration spaces is conf(n,w), the ordered configuration space of unit-diameter disks in the infinite strip of width w. The homology groups of conf(*,w) do not stabilize in the sense of Church-Ellenberg-Farb, Miller-Wilson; however, Alpert proved that when the width is 2 they stabilize in a related sense. Alpert's methods do not extend to larger widths. In this talk I discuss various notions of representation stability, and show that when the width of the strip is at least 2, the rational homology groups of conf(*,w) stabilize in a representation-theoretic sense.

No seminar

Sticky Brownian Motions are a family of correlated Brownian motions that have a tendency to stick together. They can be realized as the scaling limit of random walks in random environments and can also be viewed as random motions in a continuum-random environment. In this talk, I will present some results related to the quenched density of the motion of a particle in this continuum-random environment. In particular, I will show that under moderate deviation regime (a particular regime in between large deviation regime and diffusive regime), this quenched density after rescaling weakly converges to the solution of the stochastic heat equation with multiplicative space-time white noise. I will explain how our results shed light on the extreme behavior of Sticky Brownian Motions. This is a joint work with Hindy Drillick and Shalin Parekh.

TBA

No Seminar

Hawkes process is one of the most commonly used models for investigating the self-exciting nature of earthquake occurrences. However, seismicity patterns have complicated characteristics due to heterogeneous geology and stresses, for which existing methods with Hawkes process cannot fully capture. This study introduces novel nonparametric Hawkes process models that are flexible in three distinct ways. First, we incorporate the spatial inhomogeneity of the self-excitation earthquake productivity. Second, we consider the anisotropy in aftershock occurrences. Third, we reflect the space–time interactions between aftershocks with a non-separable spatio-temporal triggering structure. For model estimation, we extend the model-independent stochastic declustering (MISD) algorithm and suggest substituting its histogram-based estimators with kernel methods. We demonstrate the utility of the proposed methods by applying them to the seismicity data in regions with active seismic activities.

TBA

TBA

The celebrated prime geodesic theorem for a closed hyperbolic surface says that the number of closed geodesics of length at most t is asymptotically e^t/t. For a closed surface equipped with two different hyperbolic structures, Schwartz and Sharp (’93) showed that the number of free homotopy classes of length about t in both hyperbolic structures is asymptotically a constant multiple of e^{ct} /t^{3/2} for some 0