Courses and Events for Math Students and Early Career Researchers in the United States (USA)

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1
ICERM Semester Workshop: Optimal and Random Point Configurations
26 Feb 2018 - 02 Mar 2018 • Providence, RI, United States
Abstract:
This workshop will focus on probabilistic and physical aspects of systems of interacting points: their statistical mechanics, phase transitions, and ground states. Such systems include random point processes arising in probability and statistical physics in the study of random matrices, determinantal processes, zeros of random polynomials, disordered ground states, and hyperuniform systems as well as configurations satisfying a geometric or analytic optimality constraint. Special cases also involve disordered and ordered sphere packings and covering problems. While systems of interacting particles, their free energy and crystallization properties have been studied for a long time in the statistical physics community, there has also been much activity recently, both in the random matrix community and probability communities and in the complex analysis community to understand the microscopic laws of eigenvalues of random matrices and points in beta-ensembles, as well as understanding and quantifying the rigidity of related random point processes and obtaining explicit formulas for correlation functions. Large point sets with quantifiable distribution properties have long played an important role also in approximation, numerical integration, and coding theory. All these communities are seldom mixing, while these topics also link with globally and locally optimal point configurations that arise in approximation theory, including their crystallization properties. A central objective would thus be to connect the probability, statistical physics, mathematical physics and approximation theory communities.
Event listing ID:
943675
2
ICERM Semester Workshop: Fast Algorithms for Generating Static and Dynamically Changing Point Configurations
12 Mar 2018 - 16 Mar 2018 • Providence, RI, United States
Abstract:
This workshop focuses on fast algorithms for the generation of high quality point configurations and meshes such as hierarchical schemes combined with energy or geometrical optimization techniques. Energy methods utilizing appropriate potentials for a prescribed density on a given manifold have been effective in generating point configurations with good covering and packing properties. These methods rely on efficient energy, gradient, and potential computations which can be achieved by hierarchical algorithms that model a system in a recursively compressed (low-rank or low-dimensional) form where information is transmitted non-locally on a hierarchical tree structure. Different aspects of this technique can be found in the classical FFT, multigrid, and fast multipole method (FMM), as well as the recently developed fast direct solvers, multilevel models in statistics, and convolutional neural networks in deep learning. Fast generation of point configurations and meshes for dynamically evolving systems is especially challenging. For example, in molecular dynamics simulations, the shape of the molecule changes at each time step, and many numerical methods require an underlying “mesh” (e.g., points in particle methods, or surface or volume elements in finite element and integral equation methods) at each time step. Among the essential considerations are the history dependency of the meshes for simulations where the mesh needs to be updated at each time step; coupling of the fast spatial algorithms with the state-of-the-art point and mesh generation tools; recursive algorithm implementation and parallelization; and applications in atmosphere, Earth, gravitational models, dynamics of biomolecular systems; fluid dynamics, and beyond.
Event listing ID:
943696
Related subject(s):
3
ICERM Semester Workshop: Computation and Optimization of Energy, Packing, and Covering
09 Apr 2018 - 13 Apr 2018 • Providence, RI, United States
Abstract:
The packing and covering of equal geometric shapes, such as spheres or convex polyhedra, are classical geometric optimization problems. They have a long mathematical tradition and were for instance part of Hilbert's famous twenty-three problems for the 20th century. Nevertheless, seemingly simple packing and covering problems are still extremely hard to solve and generally, far from a solution. Likewise, minimal energy problems for pair potentials, of which best-packing is a special case, have many such unresolved questions. However, in recent years several new developments with computer assisted approaches have led to previously unexpected breakthrough results. These involve massive computer searches and techniques from numerical optimization, as well as the creation and application of new optimization techniques, such as specific semi-definite programming bounds. New techniques for computer assisted certified proofs allow one to obtain results that would otherwise have been difficult, if not impossible, to check.
Event listing ID:
943717
4
ICERM Semester Workshop: Computational Challenges in the Theory of Lattices
23 Apr 2018 - 27 Apr 2018 • Providence, RI, United States
Abstract:
This workshop will focus on the computational aspects of the theory of Euclidean lattices and on their applications to other areas in mathematics and computer science. It will put emphasis on computational challenges on lattice problems that have recently arisen from unexpected connections to other domains such as algebraic topology, automorphic forms, or cryptography. A major goal of this workshop is to bring together researchers from different areas, working with Euclidean lattices, and to facilitate their interactions. Topics will include the reduction theory of lattices and its applications, Voronoi algorithms and their use to compute the cohomology of arithmetic groups, the classification of lattice genera and the computation of spaces of modular forms, the algorithmic aspects of lattice based cryptography, in particular the relationship between the security of cryptographic primitives and the hardness of lattice problems.
Event listing ID:
943694
5
ICERM Topical Workshop: Birational Geometry and Arithmetic
14 May 2018 - 18 May 2018 • Providence, RI, United States
Abstract:
Recent developments in the minimal model program in positive characteristic and birational geometry have found purchase within Arithmetic Geometry, e.g., around questions of exceptional sets involved in Manin's conjecture on points of bounded height. In turn, arithmetic perspectives afforded by Manin's conjecture are starting to shed light on the geometry of spaces of rational curves. Our goal in this workshop is to bring together two camps of geometers (birational and arithmetic) who have had few opportunities to interact on a large scale. The points of contact so far are amenable to explicit computations, e.g., determination of presentations of Cox rings for Fano varieties, finite field method applications to stable rationality problems, algorithms to compute Peyre's constant in Manin's conjecture, point counts on spaces of rational curves, and these computational problems will form an important component of the workshop, which will be complemented with theoretical developments.
Event listing ID:
943715
Related subject(s):
6
GRWC — Graduate Research Workshop in Combinatorics
21 May 2018 - 01 Jun 2018 • Ames, IA, United States
Abstract:
The Graduate Research Workshop in Combinatorics (GRWC) is an annual two-week collaborative research workshop for advanced graduate students and postdocs from all areas of combinatorics. Participants work in small collaborative groups with faculty and postdocs on research problems from across the discipline. The workshops also host a variety of professional development workshops to prepare students and postdocs for industrial and academic careers.
Contact:
Email: Combinatorics.Workshop@gmail.com
Event listing ID:
942592
Related subject(s):
7
ICERM Topical Workshop: Frame Theory and Exponential Bases
04 Jun 2018 - 08 Jun 2018 • Providence, RI, United States
Abstract:
The problem of decomposing a function into a sum of simply structured functions is a classical area of research in Analysis. Exciting recent progress, e.g. the solution to the Kadison-Singer problem, results about exponential frames and Riesz bases in various settings, and results about orthogonal exponential bases for convex polytopes, has re-energized discussion in this area, opened new directions for study, and turned it into an even more active and fruitful area for research. The goal of this workshop is to discuss such new developments in this area. In particular, the workshop will focus on problems regarding exponential systems in weighted spaces and the Fuglede conjecture. Related settings will also be of interest, for example: (i) Systems of vectors obtained by translating, translating and modulating, or translating and dilating a single function over the line; (ii) Sampling and decomposition of functions in the finite dimensional setting; (iii) Sampling and interpolation of functions in analytic function spaces.
Event listing ID:
943747
Related subject(s):
8
Summer Graduate School: The ∂-Problem in the Twenty-First Century
11 Jun 2018 - 22 Jun 2018 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
This Summer Graduate School will introduce students to the modern theory of the inhomogeneous Cauchy-Riemann equation, the fundamental partial differential equation of Complex Analysis. This theory uses powerful tools of partial differential equations, differential geometry and functional analysis to obtain a refined understanding of holomorphic functions on complex manifolds. Besides students planning to work in complex analysis, this course will be valuable to those planning to study partial differential equations, complex differential and algebraic geometry, and operator theory. The exposition will be self-contained and the prerequisites will be kept at a minimum.
Event listing ID:
835335
9
ICERM Topical Workshop: Fractional PDEs: Theory, Algorithms and Applications
18 Jun 2018 - 22 Jun 2018 • Providence, RI, United States
Abstract:
Fractional partial differential equations (FPDEs) are emerging as a powerful tool for modeling challenging multiscale phenomena including overlapping microscopic and macroscopic scales. Compared to integer-order PDEs, the fractional order of the derivatives in FPDEs may be a function of space and time or even a distribution, opening up great opportunities for modeling and simulation of multi-physics phenomena, e.g. seamless transition from wave propagation to diffusion, or from local to non-local dynamics. In addition, data-driven fractional differential operators may be constructed to fit data from a particular experiment or specific phenomenon, including the effect of uncertainties. FPDEs lead to a paradigm shift, according to which data-driven fractional operators may be constructed to model a specific phenomenon instead of the current practice of tweaking free parameters that multiply pre-set integer-order differential operators. This workshop will cover all these areas, including (but not limited to) FPDE modeling, stochastic interpretation of FPDEs, efficient and accurate numerical solutions of FPDEs, mathematical analysis of FPDEs, and application of FPDE models.
Event listing ID:
943768
10
Summer Graduate School: Derived Categories
25 Jun 2018 - 06 Jul 2018 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
The goal of the school is to give an introduction to basic techniques for working with derived categories, with an emphasis on the derived categories of coherent sheaves on algebraic varieties. A particular goal will be to understand Orlov's equivalence relating the derived category of a projective hypersurface with matrix factorizations of the corresponding polynomial.
Event listing ID:
881838
Related subject(s):
11
Summer Graduate School: Representations of High Dimensional Data
08 Jul 2018 - 20 Jul 2018 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
In today's world, data is exploding at a faster rate than computer architectures can handle. This summer school will introduce students to modern and innovative mathematical techniques that address this phenomenon. Hands-on topics will include data mining, compression, classification, topic modeling, large-scale stochastic optimization, and more.
Event listing ID:
835334
12
Thirty-third Summer Conference on Topology and its Applications
17 Jul 2018 - 20 Jul 2018 • Western Kentucky University, Bowling Green, United States
Abstract:
Special sessions: Set-Theoretic Topology, Topology in Analysis and Topological Algebras (dedicated to W. W. Comfort), Topological Methods in Geometric Group Theory, Dynamical Systems and Continuum Theory, Asymmetric Topology, Applications of Knot Theory to Physical Sciences, The Interplay of Topology and Materials Properties. J. Michael Kosterlitz, recipient of the 2016 Nobel Prize in Physics "for theoretical discoveries of topological phase transitions and topological phases of matter", will give a plenary address.
Event listing ID:
966963
Related subject(s):
13
Summer Graduate School: From Symplectic Geometry to Chaos
23 Jul 2018 - 03 Aug 2018 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
The purpose of the summer school is to introduce graduate students to state-of-the-art methods and results in Hamiltonian systems and symplectic geometry. We focus on recent developments on the study of chaotic motion in Hamiltonian systems and its applications to models in Celestial Mechanics.
Event listing ID:
881858

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AIP Conference Proceedings
Last updated: 11 November 2017