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

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1
Workshop II: Mathematical and Numerical Aspects of Gravitation
25 Oct 2021 - 29 Oct 2021 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
Ever since general relativity’s birth in 1915, mathematics has had a profound impact on the way the theory has been understood: Examples over the years include Hilbert’s variational formulation, Noether’s early theorems on conservation laws, Choquet-Bruhat’s foundational well-posedness theorem and the hyperbolicity of the equations, Bondi’s concept of null infinity and gravitational waves, the incompleteness theorems of Penrose and the black hole concept, the positive energy theorem of Schoen and Yau, and the nonlinear stability of Minkowski space proven by Christodoulou and Klainerman. In more recent years, the power of numerics has added additional insights to our mathematical picture, particularly after Pretorius’s 2004 breakthrough allowing for the numerical simulation of binary black hole systems. Today, research on mathematical and numerical aspects of general relativity constitute two vibrant fields which have become very influential in the wider mathematics and physics communities. The two fields have many points of contact: Some common goals shared by both rigorous mathematical analysis and numerics include understanding the formation of black holes in gravitational collapse, their non-linear stability, and their interaction with other black holes in binary systems or other scattering processes. In their practical application to astrophysics, the two fields often play complementary roles: Numerics generates the templates which play an important part in interpreting gravitational wave detections by LIGO and VIRGO, while rigorous mathematical analysis has introduced subtle new concepts, like Christodoulou memory, which may play an important role in the next generation of detectors. Another common goal of both rigorous mathematics and of numerics, of interest to theoretical physics, is to understand generic spacetime singularities, so as to resolve in particular the celebrated weak and strong cosmic censorship conjectures of Penrose. As singularities probe the limits of the theory, a resolution of these conjectures may shed light on various attempts to transcend general relativity. Other recent problems which have brought together mathematics and numerics include work on asymptotically anti-de Sitter spacetimes, and well-posedness for alternative theories of gravity, both of interest in high energy physics. There is also recent activity on inverse problems. This workshop will gather mathematicians, theoretical physicists and numerical analysis developers to discuss these and other issues.
Topics:
Part of the Long Program Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy
Event listing ID:
1403727
2
20th Triangle Lectures in Combinatorics
14 Nov 2021 • Greensboro, NC – online, United States
Organizer:
University of North Carolina, Greensboro, NC
Abstract:
These are a series of combinatorial workshops, held once per semester, each on a Saturday. The series began with its first meeting in spring 2010. They rotate among the universities in and around the Research Triangle. Participants come from numerous colleges and universities within a few hours drive, and some from even farther away. These workshops are funded by the National Science Foundation, in particular enabling us to bring in four exciting speakers to give one hour talks each time as well as funding travel expenses for participants.
Event listing ID:
1392635
Related subject(s):
3
Workshop III: Source Inference and Parameter Estimation in Gravitational Wave Astronomy
15 Nov 2021 - 19 Nov 2021 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
Gravitational-wave (GW) observations offer a unique opportunity to study astrophysical and cosmological sources that are difficult to access through electromagnetic observations. Inferring the sources’ properties from their GW signal is one of the key objectives of GW data analysis. The planned improvements in the sensitivity of the ground-based detectors and future space-based observatories, however, bring unique computational and mathematical challenges to the inference problem including long-duration signals, high signal-to-noise ratios, increased parameter dimensionality and overlapping signals. These challenges must be overcome to fully exploit the scientific potential of GW observations. The goal of this workshop is to connect statisticians, computer scientists and GW astrophysicists to discuss the current state-of-the-art approaches to parameter estimation in GW astrophysics, and to identify the open issues to enable fast and reliable inference for different GW sources, including modelled and un-modelled signals, for the current and planned GW observatories.
Topics:
Part of the Long Program Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy
Event listing ID:
1403671
4
Workshop IV: Big Data in Multi-Messenger Astrophysics
29 Nov 2021 - 03 Dec 2021 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
Detection of gravitational waves requires the operation of very sophisticated detectors producing large amounts of data. The sensitivity of the gravitational-wave detectors to astrophysical signals is limited by the noise associated with the instruments themselves and their environment. Invaluable astrophysical information is buried in data sets that may be too large or complex to be analyzed with traditional data-processing techniques. To make the analysis of gravitational-wave detector data more efficient it becomes increasingly more important to characterize and mitigate the detector noise sources, as well as find more powerful ways to extract information from the detector data. Methods for the analysis of gravitational-wave detector data range from standard signal processing algorithms to novel machine learning algorithms. This workshop will focus on the development of these techniques for a more efficient handling of gravitational-wave data sets, reduction of detector noise, identification of astrophysical signals and increase in detection confidence. It will bring together astrophysicists, mathematicians and statisticians working on the state-of-the-art data analysis.
Topics:
Part of the Long Program Mathematical and Computational Challenges in the Era of Gravitational Wave Astronomy
Event listing ID:
1403769
5
COMD – Semester — Complex Dynamics: from special families to natural generalizations in one and several variables
18 Jan 2022 - 27 May 2022 • Berkeley, California, United States
Organizer:
MRSI – Mathematical Sciences Research Institute, Berkeley
Abstract:
Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond. Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics.
Event listing ID:
1376482
6
The Analysis and Geometry of Random Spaces
18 Jan 2022 - 27 May 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers, random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.
Event listing ID:
1423211
Related subject(s):
7
Connections Workshop: The Analysis and Geometry of Random Spaces
20 Jan 2022 - 21 Jan 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
The Connections Workshop will feature talks on a variety of topics related to the analysis and geometry of random spaces. It will preview the research themes of the semester program and will highlight the work of women in the field. There will be a panel discussion as well as other social events. This workshop is directly prior to the Introductory Workshop, and participants are encouraged to participate in both workshops. This workshop is open to all mathematicians.
Event listing ID:
1423221
Related subject(s):
8
Introductory Workshop: The Analysis and Geometry of Random Spaces
24 Jan 2022 - 28 Jan 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
This workshop will introduce some of the major themes in probability and geometric analysis that will be relevant for the semester-long program. A series of short mini-courses will give participants the opportunity to learn about important subjects such as the Schramm-Loewner evolution (SLE) or the Gaussian free field (GFF), for example. The workshop will also include "visionary" lectures by prominent researchers who will outline fruitful directions for future research.
Event listing ID:
1423329
Related subject(s):
9
Tutorials — Advancing Quantum Mechanics with Mathematics and Statistics
08 Mar 2022 - 11 Mar 2022 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
The program opens with four days of tutorials that will provide an introduction to major themes of the entire program and the four workshops. The goal is to build a foundation for the participants of this program who have diverse scientific backgrounds. For those participating in the long program, please plan to attend Opening Day on March 7, 2022 as well. Others may participate in Opening Day by invitation from the organizing committee.
Topics:
Part of the Long Program Advancing Quantum Mechanics with Mathematics and Statistics
Event listing ID:
1403768
10
Workshop I: Multiscale Approaches in Quantum Mechanics
28 Mar 2022 - 01 Apr 2022 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
This workshop will set the stage and define research directions for the rest of the program. The idea is to achieve a healthy mix between researchers developing quantum theories and methods on different spatial and temporal scales, providing a forum to discuss the advances in multiscale modeling in quantum mechanics and pave the way to stronger coupling between existing methods and completely novel quantum approaches. The main question is how to integrate already existing quantum methods to reduce their weaknesses, improve their applicability, and enable quantum calculations on much larger scales? For example, electronic orbitals obtained from density-functional theory calculations are being increasingly used to compute correlation energies using many-body Green’s function theories and explicitly correlated methods. Such synergies provide a way to approach the exact solution of the Schroedinger equation, in addition to significantly accelerating the cost of explicit many-body calculations. On a much larger spatial scales, multiscale coupling of approximate many body Hamiltonians with Maxwell’s equations allows to unify microscopic and continuum treatments of van der Waals and Casimir interactions, eventually making it possible to push the boundaries of such calculations to macroscopic systems.
Event listing ID:
1403723
11
Workshop II: Model Reduction in Quantum Mechanics
11 Apr 2022 - 15 Apr 2022 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
The first one is the rigorous mathematical derivation of reduced models from reference quantum models in some regimes such as the semiclassical limit, adiabatic limit, thermodynamic limit, and high/low density limit. New approaches have been developed in the past two decades, which lead to successful mathematical derivations of reduced models in a number of settings. However, in many settings the mathematical relations between reference and reduced models and the domain of validity of the latter still have to be clarified. The second aspect is concerned with effective interactions. Interactions between elementary particles typically have very simple functional form such as the Coulomb potential between two charged particles. However, upon solving the many-particle quantum mechanical equations, complex and intricate interactions emerge. The understanding and systematization of such interactions between composite objects provides a pathway to better understand quantum mechanics itself and constitutes the basis for developing coarse-grained approaches to describe interactions in large quantum systems. The third aspect is about simplified quasiparticle or collective mode descriptions of complicated quantum states, using one-particle spin-orbitals, plasmons, phonons, polarons, or excitons. Such objects are embedded in finite or infinite dimensional Hilbert spaces defined by the basis set utilized to expand the many-body wavefunction. Recently, many interesting efforts have been dedicated to analyzing and visualizing quantum states in Hilbert spaces, as well as to map and embed Hilbert spaces between different quantum systems. Such mapping and embedding of Hilbert spaces brings out novel insights into the intricate nature of quantum fluctuations and should ultimately allow to develop better and more reliable approximations for solving complex quantum systems.
Event listing ID:
1403711
12
Workshop III: Large-Scale Certified Numerical Methods in Quantum Mechanics
02 May 2022 - 06 May 2022 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
Simulating very large quantum systems require new numerical methods and algorithms. Such simulations indeed lead to solving linear and nonlinear systems of equations and eigenvalue problems, that are characterized by high dimensionality, large ranks (for tensor problems), and extreme scale. They must exploit massive parallelism in both space and time and rank-reduction methods, through deterministic or stochastic approaches, optimized data structures, and minimize communication. It is also key to have tools at hands to assess the quality of the simulation results. Error analysis is of major relevance in the simulation of quantum systems, but to date, it has received less attention than in other fields such as fluid or structure dynamics. The error between the exact and computed values of a given physical quantity of interest (QOI), e.g. the dissociation energy of a molecule, has several origins: a model error (resulting from the choice of a computationally tractable, but not extremely accurate, model, e.g. Kohn-Sham with B3LYP functional), a discretization error (resulting from the choice of a finite basis set), an algorithmic error (due to the choice of stopping criteria in Self-Consistent Field and other iterative algorithms), an implementation error (due to possible bugs or uncontrolled round-off errors), a computing error (due to random hardware failures). Quantifying these different sources of errors is key for two reasons. First, guaranteed estimates on these five components of the error would allow one to supplement the computed value of the QOI returned by the numerical simulation with guaranteed error bars (certification of the result). Second, this would allow one to choose the parameters of the simulation (approximate model, discretization parameters, algorithm and stopping criteria, data structures?) in an optimal way in order to minimize the computational effort required to reach the target accuracy (error balancing). Since molecular simulation consumes a massive amount of CPU time in scientific research centers worldwide, this would have a major impact on the use of scientific computing resources.
Event listing ID:
1403798
13
Hot Topics Workshop — Topological and Dynamical Analysis of Brain Connectomes
14 May 2022 - 15 May 2022 • Providence, RI, United States
Organizer:
The Institute for Computational and Experimental Research in Mathematics (ICERM)
Abstract:
With the substantial recent progress in connectomics, the study of comprehensive maps of nervous systems, much more is known about the connectivity structure of brains. This has led to a multitude of new questions about the relationship between connectivity patterns, neural dynamics and brain function, many of which lead to new mathematical problems in graph theory and dynamics on graphs. The goal of this workshop is to bring together a broad range of researchers from neuroscience, physics, mathematics, and computer science to discuss new challenges in this emergent field and promote new collaborations.
Event listing ID:
1436205
14
Workshop IV: Monte Carlo and Machine Learning Approaches in Quantum Mechanics
23 May 2022 - 27 May 2022 • Los Angeles, CA, United States
Organizer:
IPAM - Institute for Pure & Applied Mathematics, an NSF Math Institute at UCLA
Abstract:
Quantum mechanics has strong connections with probability theory and statistics. Quantum states are amenable to probabilistic interpretation based on laws of statistics. Many quantum problems can be reformulated in terms of Feynman’s path integral formulation, which amounts to computing quantum partition functions using statistical sampling techniques. In addition, new statistical learning approaches are emerging that aim to incorporate “quantumness” to ensure unitarity and long-range correlations that are so ubiquitous in quantum systems. Considering these recent developments, it appears timely to bring together the large community of people working on quantum systems and statistical techniques. This workshop will broadly address the reaches and limitations of statistics as applied to the modeling and understanding of quantum systems and highlight examples where quantum and statistical models enhance each other.
Event listing ID:
1403819
15
Summer Graduate School — Integral Equations and Applications
06 Jun 2022 - 18 Jun 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
The field of Integral Equations has a long and distinguished history, being the driving force behind many fundamental developments in various areas of mathematics including Harmonic Analysis, Partial Differential Equations, Potential Theory, Scattering Theory, Functional Analysis, Complex Analysis, Operator Theory, Mathematical Physics and Numerical Analysis.
Event listing ID:
1443882
16
MSRI-UP 2022 — Algebraic Methods in Mathematical Biology
13 Jun 2022 - 23 Jul 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
The MSRI Undergraduate Program (MSRI--UP) is a comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.
Event listing ID:
1443936
17
Summer Graduate School — Random Graphs
05 Jul 2022 - 16 Jul 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many real-world networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi. Spurred by these findings, many novel models have been introduced and properties have been investigated.
Event listing ID:
1443988
18
Summer Graduate School — Algebraic Theory of Differential and Difference Equations, Model Theory and their Applications
05 Jul 2022 - 16 Jul 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Event listing ID:
1443910
19
Topical Workshop — Lean for the Curious Mathematician 2022
11 Jul 2022 - 15 Jul 2022 • Providence, RI, United States
Organizer:
The Institute for Computational and Experimental Research in Mathematics (ICERM)
Abstract:
At the ICERM workshop "Lean for the Curious Mathematician 2022", experts in the Lean theorem prover will explain how to do number theory, topology, geometry, analysis, and algebra in the Lean theorem prover. This will be accessible to mathematicians without a specific background in computer-proof systems. The material covered will range from undergraduate mathematics to modern research. Participants will be invited to begin formalizing mathematical objects from their own research.
Event listing ID:
1436259
20
Homotopical Methods in Fixed Point Theory
11 Jul 2022 - 15 Jul 2022 • Boulder, CO, United States
Organizer:
University of Colorado Boulder
Abstract:
The goal of this summer school is to introduce participants to tools and ideas from algebraic topology and homotopy theory that are used in the study of fixed point theory. This will be a problem set focused summer school surrounding four mini-courses.
Topics:
1) Fixed point theory and Nielsen theory 2) Categorical Approach to Duality 3) Spectra 4) Trace Methods
Abstract submission deadline:
01 Feb 2022
Event listing ID:
1448829
Related subject(s):
21
Summer Graduate School — 2022 Joint PCMI School: Number Theory Informed by Computation
18 Jul 2022 - 07 Aug 2022 • PCMI - Park City Mathematics Institute, Park City, Utah, United States
Abstract:
The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.
Event listing ID:
1443973
22
Summer Graduate School — Topological Methods for the Discrete Mathematician
25 Jul 2022 - 06 Aug 2022 • St. Mary's College, Moraga, California , United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
The summer school will lead participants from appealing, simple-to-state problems at confluence of combinatorics, geometry, and topology to sophisticated topological methods that are required for their resolution. In recent years topological methods have found numerous novel applications in mathematics and beyond, such as in data science, machine learning, economics, the social sciences, and biology. The problems we will discuss are particularly well-suited to rapidly put students in a position to approach related research questions.
Event listing ID:
1443970
Related subject(s):
23
Summer Graduate School — Tropical Geometry
01 Aug 2022 - 13 Aug 2022 • St. Mary's College, Moraga, California , United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory.
Event listing ID:
1444034
Related subject(s):
24
Analytic and Geometric Aspects of Gauge Theory (GT)
22 Aug 2022 - 21 Dec 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Abstract:
The mathematics and physics around gauge theory have, since their first interaction in the mid 1970's, prompted tremendous developments in both mathematics and physics. Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories. This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology. Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications. The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.
Event listing ID:
1423400
25
Workshop — Introductory Workshop: Floer Homotopy Theory
12 Sep 2022 - 17 Sep 2022 • Mathematical Sciences Research Institute, Berkeley, United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
Over the last decade, there has been a wealth of new applications of homotopy-theoretic techniques to Floer homology in low-dimensional topology and symplectic geometry, including Manolescu’s disproof of the high-dimensional Triangulation Conjecture and Abouzaid-Blumberg’s proof of the Arnol’d Conjecture in finite characteristic. Conversely, results in Floer theory and categorification have opened new directions of research in homotopy theory, from string topology to S-Lie algebras. The goal of this workshop is to introduce researchers in Floer theory to modern techniques and questions in homotopy theory and, conversely, introduce researchers in homotopy theory to ideas underlying Floer theory and its applications.
Event listing ID:
1444030
Related subject(s):
26
Introductory Workshop: Algebraic Cycles, L-Values, and Euler Systems
23 Jan 2023 - 28 Jan 2023 • Mathematical Sciences Research Institute, Berkeley, United States
Organizer:
Mathematical Sciences Research Institute (MRSI)
Abstract:
The Introductory Workshop aims to provide a coherent overview of current research in algebraic cycles, L-values, Euler systems, and the many connections between them. This includes the study of special cycles on Shimura varieties and moduli spaces of shtukas, integral representations of L-values and the construction of p-adic L-functions, and the construction of Euler systems from special elements in Chow groups or higher Chow groups of Shimura varieties. Workshop lectures will be organized into short lecture series, so as to allow each series to begin with expository lectures on foundational results before moving on to current research.
Event listing ID:
1444125
Related subject(s):


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Last updated: 14 October 2021