Organizing Committee
 Dmitriy Bilyk
University of Minnesota  Xuemei Chen
University of North Carolina Wilmington  Emily King
Colorado State University  Dustin Mixon
Ohio State University  Kasso Okoudjou
Tufts University
Abstract
Certain problems in mathematics, physics, and engineering are formulated as minimizing cost functions that take as input a set of points on a compact manifold. In applied and computational harmonic analysis one is usually interested in finding tight frames and equiangular tight frames, which are respectively minimizers of different cost functions. In quantum information theory, the study of SICPOVMS is equivalent to the existence of a point configuration made of antipodal points on a complex sphere. There seems to be a phenomenon where highly symmetric configurations are optimizers and optimizers often exhibit (partial) symmetries. The theory of spherical designs in combinatorics and discrete geometry with applications in approximation theory in the form of cubature formulas is deeply related to point configurations and distributions. Training a neural network involves minimizing a cost function relating to the desired task; it was recently discovered that doing so often results in the last layer of the neural network corresponding to an optimal configuration of points on a sphere, a phenomenon called neural collapse.
Numerical solutions to optimization problems are used to study the putative geometric and arithmetic structure of the corresponding optimal configurations. Linear programming bounds have been a major tool in point configurations and led to the recent breakthrough in sphere packing problems in dimensions 8 and 24. Semidefinite programming is used to find exact solutions of maximal twodistance sets. Many spherical designs and point distribution problems are motivated by numerical integration and interpolation. Moreover, understanding neural collapse requires an understanding of the training of neural networks. As such, there is a need to expand the use of numerical and computational methods to solve these problems. Our goal is to provide a forum to explore problems in point configurations and distributions from the various aforementioned perspectives.
Confirmed Speakers & Participants
Talks will be presented virtually or inperson as indicated in the schedule below.
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Manuchehr Aminian
California State Polytechnic University, Pomona

Igor Balla
Masaryk University

Radel BenAv
Holon Institute of Technology

Dmitriy Bilyk
University of Minnesota

Bernhard Bodmann
University of Houston

Sergiy Borodachov
Towson University

Dongwei Chen
Clemson University

Peter Dragnev
Purdue University Fort Wayne

Giacomo Elefante
University of Torino

Kean Fallon
Iowa State University

Damir Ferizovic
KU Leuven

Matthew Fickus
Air Force Institute of Technology

Simon Foucart
Texas A&M University

Christina Frederick
New Jersey Institute of Technology

Alexey Glazyrin
University of Texas Rio Grande Valley

Assaf Goldberger
Tel Aviv University

Peter Grabner
Technische Universität Graz

Shuang Guan
Tufts University

Douglas Hardin
Vanderbilt University

Alex Iosevich
University of Rochester

Joseph Iverson
Iowa State University

John Jasper
Air Force Institute of Technology

Ian Jorquera
Colorado State University

Emily King
Colorado State University

Gene Kopp
Louisiana State University

Nathan Mankovich
University of Valencia

Ryan Matzke
Vanderbilt University

Azita Mayeli
City University of New York

Dustin Mixon
Ohio State University

Yonah Moise
Tufts University

Oleg Musin
University of Texas Rio Grande Valley

Nicolas Nagel
Chemnitz University of Technology

Joel Nathe
Purdue University

Tom Needham
Florida State University

Kaysie O'Hanian
Iowa State University

Kasso Okoudjou
Tufts University

Vignon Oussa
Bridgewater State University

Daniel Riley
Tufts University

Ian Ruohoniemi
University of Minnesota

Kylie Schnoor
Colorado State University

David Shirokoff
New Jersey Institute of Technology

Clayton Shonkwiler
Colorado State University

Reed Spitzer
Brown University

Tetiana Stepaniuk
Institute of Mathematics of National Academy of Sciences of Ukraine

Antonio Torres
UCDavis

Oleksandr Vlasiuk
PTC

Xuming Xie
Morgan State University

Yukun Yue
University of Wisconsin, Madison
Workshop Schedule
Monday, June 3, 2024

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

9:00  9:45 am EDTIntro Talk11th Floor Lecture Hall
 Dmitriy Bilyk, University of Minnesota
 Xuemei Chen, University of North Carolina Wilmington
 Emily King, Colorado State University
 Dustin Mixon, Ohio State University
 Kasso Okoudjou, Tufts University

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

10:30  11:15 am EDTOptimization Informed by Geometric Invariant Theory and Symplectic Geometry11th Floor Lecture Hall
 Speaker
 Clayton Shonkwiler, Colorado State University
 Session Chair
 Dustin Mixon, Ohio State University
Abstract
Optimal configurations can typically be realized as minimizers of some cost function. While in general the function can have many local minima, making it challenging to search for minimizers numerically, some cost functions which have natural interpretations in geometric invariant theory and symplectic geometry are surprisingly simple to optimize despite being nonconvex. The goal in this talk is to explain some of the geometric context, and then to illustrate this approach with some applications, including to equalnorm Parseval frames, tight fusion frames, and normal matrices. This is joint work with Tom Needham and partially with Dustin Mixon and Soledad Villar.

11:30 am  12:15 pm EDTTopology of Spaces of Structured Vector Configurations11th Floor Lecture Hall
 Speaker
 Tom Needham, Florida State University
 Session Chair
 Dustin Mixon, Ohio State University
Abstract
This talk will provide an overview of recent work describing the topology of various spaces of structured configurations of vectors; for example, spaces of unit norm tight frames or spaces of normal matrices with additional constraints. Our work is largely based on the observation that these spaces arise naturally from the perspective of symplectic geometry, allowing for the application of powerful results from that field. I will explain the general ideas that we use from symplectic geometry, and illustrate them on concrete spaces of interest. I will also describe recent results on frames on manifolds — that is, structured collections of vector fields — where the topological questions become much more subtle.

12:30  2:00 pm EDTNetworking LunchWorking Lunch  11th Floor Collaborative Space

2:00  2:45 pm EDTOptimally arranging twice as many lines as the ambient dimension11th Floor Lecture Hall
 Speaker
 Joseph Iverson, Iowa State University
 Session Chair
 Emily King, Colorado State University
Abstract
We discuss the problem of optimally arranging 2d lines (1dimensional subspaces) through the origin of C^d. Specifically, we conjecture that the Welch can always be attained in this setting, and we present new explicit constructions of equiangular tight frames that perform this feat.

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

3:30  4:15 pm EDTThe SDP and LP bounds for optimal spherical configurations using their distance distribution11th Floor Lecture Hall
 Speaker
 Oleg Musin, University of Texas Rio Grande Valley
 Session Chair
 Emily King, Colorado State University
Abstract
In this talk a new extension of known semidefinite and linear programming upper bounds for spherical codes will be presented and consider a version of this bound for distance graphs. The main result can be applied for the distance distribution of a spherical code, and it will be shown that this method can work effectively. In particular, I get a shorter solution to the kissing number problem in dimension 4. I will consider reasonable approaches for a solutions of two long standing open problems: the uniqueness of maximum kissing arrangements in 4 dimensions and the 24cell conjecture. In a recent preprint by de Laat  Leijenhorst  de Muinck Keizer claimed a solution to the uniqueness problem. We will also discuss their approach.

4:30  6:00 pm EDTReception11th Floor Collaborative Space
Tuesday, June 4, 2024

9:00  9:45 am EDTNew strongly regular graphs from optimal line packings11th Floor Lecture Hall
 Speaker
 John Jasper, Air Force Institute of Technology
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
In this talk, we'll explore several new constructions of strongly regular graphs. Specifically, we will show how some known optimal line packings can be coerced into generating new families of SRGs. We will also introduce a new construction of optimal line packings, yielding additional infinite families of SRGs.

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

10:30  11:15 am EDTA constructive approach to Zauner's conjecture via the Stark conjectures11th Floor Lecture Hall
 Speaker
 Gene Kopp, Louisiana State University
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
We describe work towards a construction of d^2 equiangular lines in ddimensional complex Hilbert space (equivalently, a SICPOVM) from special values of complex analytic functions. A leading role is played by certain functionvalued cocycles for subgroups of SL_2(Z), which arise in both number theory and quantum field theory. The remaining obstacles are two unproven conjectures and the presence of a noncontinuous Galois automorphism in the construction. Despite these obstacles, the construction has been implemented to produce new examples of SICPOVMs. This talk covers joint work with Marcus Appleby and Steven Flammia and may also cover joint work with Jeffrey Lagarias.

11:30 am  12:15 pm EDTMaximal Projection Constants and Existence of Maximal ETFs11th Floor Lecture Hall
 Speaker
 Simon Foucart, Texas A&M University
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
After introducing the concepts of minimal projections and maximal projection constants, we highlight some reformulated expressions for the maximal relative projection constants which are more amenable to numerical computations. From here, we derive upper estimates for the maximal relative projection constants that turn into equalities when and only when equiangular tight frames exist. As shown by Deregowska and Lewandowska, a similar equivalence holds between mth maximal absolute projection constants and maximal equiangular tight frames in dimension m, hence essentially rephrasing (the weak form of) Zauner's conjecture in terms of the values of the maximal absolute projection constants in the complex setting. In the real setting, where maximal equiangular tight frames can fail to exist, we present supporting evidence for our speculated value of the fifth maximal absolute projection constant, exploiting in particular the notion of real mutually unbiased equiangular tight frames.

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

12:30  2:00 pm EDTLunch/Free Time

2:00  2:45 pm EDTHarmonic and RadonHurwitz equiisoclinic tight fusion frames11th Floor Lecture Hall
 Speaker
 Matthew Fickus, Air Force Institute of Technology
 Session Chair
 Dmitriy Bilyk, University of Minnesota
Abstract
Every equiisoclinic tight fusion frame (EITFF) is a type of optimal Grassmannian code, and yields a collection of isometries with minimal block coherence. We discuss two recent projects involving EITFFs. The first is joint work with John Jasper, Joey Iverson and Dustin Mixon. We characterize when an EITFF arises as the orbit of a single subspace under the action of a finite abelian group of unitary operators. This yields new EITFFs, and generalizes the wellknown equivalence between harmonic equiangular tight frames and difference sets. The second is joint work with Enrique GomezLeos and Joey Iverson. We generalize some classical results of Lemmens and Seidel to the complex setting, fully characterizing the existence of EITFFs whose subspaces have dimension equal to exactly half of that of the ambient space. We moreover show that all such EITFFs are necessarily highly symmetric.

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

3:30  4:15 pm EDTLinear Programming Bound Solutions to the Continuum Pairwise Particle Interaction Energy11th Floor Lecture Hall
 Speaker
 David Shirokoff, New Jersey Institute of Technology
 Session Chair
 Dmitriy Bilyk, University of Minnesota
Abstract
We examine the problem of minimizing the continuum nonlocal, nonconvex variational problem that arises from modeling a large number of pairwise interacting particles in the presence of thermal noise (i.e., molecular dynamics). Determining global minima (ground states) to these functionals is important as they characterize the structure of matter, selfassembly, and phase transitions in materials. Determining global minima is, however, in general difficult. We will derive linear programming (LP) lower bounds in the spirit of Cohn and Kumar via a dual approach as convex relaxations over closed subsets of probability measures. We will then present solutions to the LP bounds for several interaction kernels inspired by molecular dynamics – the Morse potential and an Onsagar potential from liquid crystals. We will also discuss several discrete cases where the minimizers are provably sharp and counter examples where the LP bound fails to be a tight lower bound.
Wednesday, June 5, 2024

9:00  9:45 am EDTOptimal real or complex sphere packings by zeromean tensor embeddings11th Floor Lecture Hall
 Speaker
 Bernhard Bodmann, University of Houston
 Session Chair
 Emily King, Colorado State University
Abstract
This talk is concerned with achieving optimal coherence for highly redundant real or complex unitnorm frames. When the number of vectors in a frame becomes too large to admit equiangular arrangements, other geometric optimality criteria need to be identified. The key idea for these results is iterating the embedding technique by Conway, Hardin and Sloane. As a consequence of their work, a quadratic mapping embeds equiangular lines into a simplex in a real Euclidean space. Here, higher degree polynomial maps embed highly redundant unitnorm frames to simplices in highdimensional Euclidean spaces. This talk focuses on the lowest degree maps and extends earlier work with John Haas on the real case.

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

10:30  10:40 am EDTControl of Instability in a VlasovPoisson System Through an External Electric FieldLightning Talks  11th Floor Lecture Hall
 Speaker
 Yukun Yue, University of Wisconsin, Madison
 Session Chair
 Emily King, Colorado State University
Abstract
Plasma can get very unstable: Minor perturbations to equilibrium states can potentially instigate rapid growth, resulting in substantial disruptions of the equilibrium. Deploying external electric field to suppress such instabilities is a desirable demand in numerous practical applications, but also a very challenging task. We use the VlasovPoisson equation as a fundamental model that simulates plasma dynamics, and aim at designing external fields to suppress the TwoStream and BumponTail instabilities, two celebrated unstable equilibrium in plasma physics. Specifically, we introduce a comprehensive framework that employs linear stability analysis to engineer an external field aimed at counteracting poles within the complex plane, thereby averting solutions that tend toward infinity. Additionally, we note that an external field designed to naturally oppose the electric field can lead the plasma towards a freestreaming flow characterized by exponential decay. Our demonstrations reveal that both methodologies yield computationally favorable outcomes. Furthermore, we establish that the initial approach, when applied with a particular counteracting function, inherently gives rise to the second approach.

10:40  10:50 am EDTSmall codesLightning Talks  11th Floor Lecture Hall
 Speaker
 Igor Balla, Masaryk University
 Session Chair
 Emily King, Colorado State University
Abstract
In 1955, Rankin resolved the classical problem of determining the maximum number of unit vectors in R^r with no pairwise inner product exceeding alpha for all alpha ≤ 0 and more recently, Bukh and Cox asked about what happens when alpha is slightly bigger than 0. In this talk, we will answer their question by showing that the maximum is (2 + o(1))r for all 0 ≤ alpha ≪ r^(2/3), where the exponent 2/3 is best possible. As a consequence, we obtain an upper bound on the size of a qary code with block length r and distance (1  1/q)r  o(r^(1/3)), which is tight up to the multiplicative factor 2(1  1/q) + o(1) for any prime power q and infinitely many r. When q = 2, this resolves a conjecture of Tietäväinen from 1980 in a strong form. Time permitting, we will mention how our result translates to setcoloring Ramsey numbers via a recently discovered connection.

10:50  11:00 am EDTOn the L2discrepancy of latin hypercubesLightning Talks  11th Floor Lecture Hall
 Speaker
 Nicolas Nagel, Chemnitz University of Technology
 Session Chair
 Emily King, Colorado State University
Abstract
Motivated by the asymptotic optimality of van der Corput point sets and Fibonacci lattices with respect to discrepancy we study more general point sets constructed from permutations. In this direction, generalizing a result already observed by Hinrichs, Kritzinger and Pillichshammer for van der Corput point sets and rational lattices, we show that the periodic and extremal L2discrepancy of permutation sets are related to each other by a precise equality. This result can be generalized to arbitrary dimensions when working with point sets constructed from latin hypercubes. We also obtain asymptotically tight bounds on the optimal periodic L2 discrepancy of latin hypercubes for dimensions d>2.

11:00  11:10 am EDTUniform distribution via lattices: from point sets to sequencesLightning Talks  11th Floor Lecture Hall
 Speaker
 Damir Ferizovic, KU Leuven
 Session Chair
 Emily King, Colorado State University
Abstract
I will show how to construct computationally simple sequences S in the ddimensional hypercube with base b. For d = 1 these will be (generalized) van der Corput sequences. Further, I will introduce the notion of f subadditivity and use it to define a very general notion of discrepancy function D which serves as an umbrella term that covers the Lp discrepancy, Wasserstein pdistance, and many more methods to compare empirical measures to an underlying base measure. I will use these concepts to prove novel bounds of the Lp discrepancy of van der Corput sequences in terms of digit sums. This talk is based on the paper with the same title: https://arxiv.org/abs/2308.13297

11:10  11:20 am EDTSteifel Packings for Coherent CommunicationsLightning Talks  11th Floor Lecture Hall
 Speaker
 Nathan Mankovich, University of Valencia
 Session Chair
 Emily King, Colorado State University
Abstract
We present a new algorithm that computes packings on the Stiefel manifold for multiinput multioutput coherent communications. This algorithm builds upon an algorithm by AlvarezVizoso et al. for Grassmannian packings and leverages the Riemannian geometry of the Stiefel manifold by optimizing with gradient descent on the Steifel manifold. We apply this algorithm to generate new Steifel packings and compare them to other packings for coherent communications.

11:20  11:30 am EDTPaleyWiener Theorem for Probabilistic FramesLightning Talks  11th Floor Lecture Hall
 Speaker
 Dongwei Chen, Clemson University
 Session Chair
 Emily King, Colorado State University
Abstract
The PaleyWiener Theorem is a classical result about the stability of basis in Banach spaces claiming that if a sequence is close to a basis, then this sequence is a basis. Similar results are extended to frames in Hilbert spaces. As the extension of finite frames for $\mathbb{R}^d$, probabilistic frames are probability measures on $\mathbb{R}^d$ with finite second moments and the support of which span $\mathbb{R}^d$. This paper generalizes the PaleyWiener theorem to the probabilistic frame setting. We claim that if a probability measure is close to a probabilistic frame in some sense, this probability measure is also a probabilistic frame.

11:30  11:45 am EDTMinmax polarization property of sharp spherical codes that are not tight designsLightning Talks  11th Floor Lecture Hall
 Speaker
 Sergiy Borodachov, Towson University
 Session Chair
 Emily King, Colorado State University

11:45 am  12:00 pm EDTOptimal polarization (PULB) pairs of codes found in the Leech latticeLightning Talks  11th Floor Lecture Hall
 Speaker
 Peter Dragnev, Purdue University Fort Wayne
 Session Chair
 Emily King, Colorado State University
Abstract
It was previously shown by the authors that the discrete potentials of almost all known sharp codes attain universal lower bounds for polarization (PULB) for spherical $\tau$designs, where “universal” is meant in the sense of applying to a large class of potentials that includes absolutely monotone functions of inner products and in the sense that the computational parameters of the bound are invariant with respect to the potential. In this talk we characterize the sets of universal minima D for some of these sharp codes $C$ found in the Leech lattice and establish a duality relationship, namely that the normalized discrete potentials of $C$ and $D$ have the same minimum value and the sets $C$ and $D$ are each others minima sets (up to antipodal symmetrization in some cases). The extremal duality is obtained by utilizing the natural embedding of the PULB pair codes in the Leech lattice and its properties, which simplifies the analysis significantly. In the process we discover a new universally optimal code in $\mathbb{RP}^{21}$ with $1408$ points.

12:30  2:00 pm EDTLunch/Free Time

2:00  2:45 pm EDTLinear programming bounds for periodic point configurations.11th Floor Lecture Hall
 Speaker
 Doug Hardin, Vanderbilt University
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
We develop “linear programming” bounds for the energy of lattice periodic configurations in Euclidean space and prove the optimality of two A2periodic configurations in the plane (one with four generators and and with six generators) for all energy functionals with rapid decay arising from completely monotone functions of distance squared; i.e., these are universally optimal (in the language of Cohn and Kumar) amongst all A2 periodic configurations with the same number of generators. This is joint work with Nate Tenpas.

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

3:30  4:15 pm EDTGeodesic Riesz Energy on Spheres and Projective Spaces11th Floor Lecture Hall
 Speaker
 Ryan Matzke, Vanderbilt University
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
One way of finding an "optimal" point configuration is to determine one that maximizes the sum of pairwise distances between distinct points. Specifically in the case of Euclidean distance on the sphere, such point sets are uniformly distributed, minimize the quadratic spherical cap discrepancy (which is equivalent to a certain worst case error estimate) over all point sets of the same cardinality. However, for other metrics on other spaces, such as geodesic distances on spheres or projective spaces, maximizing the sum of distances may not result in uniformly distributed point sets. We will discuss what is known in these settings, as well as recent progress in determining optimizers of the more general Geodesic Riesz energies on these spaces.
Thursday, June 6, 2024

9:00  9:45 am EDTA few simple perspectives on Fourier uncertainty11th Floor Lecture Hall
 Speaker
 Alex Iosevich, University of Rochester
 Session Chair
 Dmitriy Bilyk, University of Minnesota
Abstract
We will discuss some simple perspectives on Fourier uncertainty from the point of view of exact signal recovery. The main theme is that one always has a stronger uncertainty principle in the presence of nontrivial Fourier restriction estimates. Arithmetic aspects of the problem will be discussed as well.

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

10:30  11:15 am EDTLine Configurations, Automorphisms and Cohomology11th Floor Lecture Hall
 Speaker
 Assaf Goldberger, Tel Aviv University
 Session Chair
 Dmitriy Bilyk, University of Minnesota
Abstract
(Joint with R. BenAv, X. Chen, G. Dula, K. Okoudjou) Some recent papers discuss a method of generation of complex line configurations from association schemes. If the scheme is Schurian, subordinate to a group G, then G is an automorphism subgroup of the configuration. However, G then acts on the points, without rephasing. In this work we propose an extension to weighted Schemes, which introduces G actions that involve rephasing. Our extension may also accommodate algebraic configurations, in which G is also allowed to act by Galois transformations. This construction involves the study of the cohomology groups of G and of certain subgroups, and is closely related to arithmetic invariants, like the Brauer group.

11:30 am  12:15 pm EDTCONSTRUCTING AND CLASSIFYING THE SPACE OF SMALL INTEGER WEIGHING MATRICES11th Floor Lecture Hall
 Speaker
 Radel BenAv, Holon Institute of Technology
 Session Chair
 Dmitriy Bilyk, University of Minnesota
Abstract
We describe an algorithm for generating all the possible PIW(m, n, k)  integer m × n Weighing matrices of weight k up to Hadamard equivalence. Our method relies on properties of a specific matrix ordering, and the results can used for classification of isomorphism classes of integer matrices. Our method is efficient on a personal computer for small size matrices, up to m ≤ n = 12, and k ≤ 50. As a by product we also improved the nsoks [12] algorithm to find all possible representations of an integer k as a sum of n integer squares. We have implemented our algorithm in Sagemath and as an example we provide a complete classification for n = m = 7 and k = 25. Our list of IW(7, 25) can serve as a step towards finding the open classical weighing matrix W(35, 25).

12:30  2:00 pm EDTOpen Problems LunchWorking Lunch  11th Floor Collaborative Space

2:00  2:45 pm EDTNew results on the HRT Conjecture11th Floor Lecture Hall
 Speaker
 Vignon Oussa, Bridgewater State University
 Session Chair
 Dustin Mixon, Ohio State University
Abstract
This talk explores a subcase of the HeilRamanathanTopiwala (HRT) conjecture, which proposes that a set of any finite timefrequency shifts of a nonzero squareintegrable function is linearly independent. We identify and discuss certain sufficient conditions, focusing on the rational dimension of a particular vector space and the size of the zero set of the Zak transform under which the conjecture remains valid. A notable implication of our main result is the successful resolution of a case of the HRT subconjecture, originally proposed by Chris Heil.

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

3:30  4:15 pm EDTRecent developments in the eigenvalue distribution of sparsespectral limiting operators11th Floor Lecture Hall
 Speaker
 Azita Mayeli, City University of New York
 Session Chair
 Dustin Mixon, Ohio State University
Abstract
In this presentation, we will address the motivation behind studying the eigenvalue distribution of spatiofrequency limiting operators and provide an overview of the recent developments in this area.
Friday, June 7, 2024

9:00  9:45 am EDTOrthonormal bases and minimizers of the pframe energy on spheres11th Floor Lecture Hall
 Speaker
 Alexey Glazyrin, University of Texas Rio Grande Valley
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
The pframe potential for a pair of unit vectors x, y is defined as <x,y>^p. The general problem is to determine a minimizing point configuration of a given size for a given p. In the talk I will give a brief overview of this problem and its analog for measures and show several new results for 0<p<2. In particular, I will explain why measures whose support is an orthonormal basis are local minimizers of the pframe energy and use this result to resolve the conjecture of Ben Av, Chen, Goldberger, Kang, and Okoudjou.

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

10:30  11:15 am EDTVariational problems from electrostatics, contact mechanics, and physics of ferromagnetic materials11th Floor Collaborative Space
 Speaker
 Oleksandr Vlasiuk, PTC
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
We will discuss some optimization problems originating in physics. Nonisotropic interactions depending not only on the distances between interacting particles, but also on their relative positions will be of special interest. This presentation is partly based on the joint work with J. Batle and O. Ciftja.

11:30 am  12:15 pm EDTHYPERUNIFORMITY AND ENERGY ON PROJECTIVE SPACES11th Floor Lecture Hall
 Speaker
 Peter Grabner, Technische Universität Graz
 Session Chair
 Kasso Okoudjou, Tufts University
Abstract
Joint work with: A. Anderson, D. Bilyk, B. Borda, J. Brauchart, M. Dostert, R. Matzke, T. Stepaniuk We study Riesz, Green and logarithmic energy on twopoint homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for the mentioned energies using determinantal point processes. Moreover, we determine lower bounds for these energies. Furthermore, we extend the notion of hyperuniformity to the projective spaces and study the connection between energy and the Wasserstein distance.

12:30  2:00 pm EDTLunch/Free Time

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