Konferenzen  >  Mathematik  >  Geometrie und Topologie  >  Vereinigte Staaten

American Institute of Mathematics (AIM)

This workshop, sponsored by AIM and the NSF, will be devoted to recent developments in the study of Lagrangian Floer theory of symmetric products of Riemann surfaces and Hilbert schemes of symplectic 4-manifolds, and their applications both to symplectic topology and the low dimensional topology.

American Mathematical Society

Diophantine equations are systems of polynomial equations solved over integers or rational numbers. Diophantine geometry is the study of Diophantine equations using ideas and techniques from algebraic geometry. It is one of the oldest subjects of mathematics and the most popular part of number theory connecting it to algebraic geometry.

The goal of this session is to explore recent developments in the theory of arithmetic geometry and with special focus on curves and Jacobian varieties. We intend to bring together mathematicians, working on this area of research, from the USA and from Europe encouraging further cooperation and discussion. We will especially encourage younger mathematicians and graduate students and newcomers in the area.

The session will focus on the following topics, but we will be open and welcoming to talks which do not fall in the list of topics below.

Tel.: [2477607447];     Email: shaska@risat.org

algebraic curves, Abelian varieties, isogenies, torsion points, Tate modules, heights, weighted heights, height conjectures, Brauer group, K3 surfaces, Kummer varieties, Néron-Tate heights, Minimal models, minimal height, Néron models, Brauer-Siegel theorem, Mordell-Lang conjecture, Mordell-Weil, Bombieri-Lang conjecture, Vojta’s conjecture

Zahlentheorie, Arithmetik,    Algebra

In this workshop we will study surfaces in 3-manifolds from several perspectives. Each participant will be asked to give a 2-hour lecture.

Potential subtopics include but are not limited to: Virtual Haken, Character variety methods, Foliations, Minimal surfaces, Totally geodesic surfaces

Mathematical Sciences Research Institute (MSRI)

This workshop will highlight talks on various aspects of Diophantine Geometry. The goal of the workshop is to bring together researchers at different career stages and of various backgrounds in order to establish new collaborations and mentoring relationships.

Mathematical Sciences Research Institute (MSRI)

This workshop will feature expository lectures about current developments in Diophantine geometry. This includes the uniform Mordell—Lang for rational points on curves, the Andre—Oort conjecture for special points on Shimura varieties, and effective results via Chabauty method, and related topics in Arakelov theory, unlikely intersections, arithmetic statistics, arithmetic dynamics, and p-adic Hodge theory.

Algebra,    Zahlentheorie, Arithmetik

ICERM

Discrete periodic Schrodinger operators describe the behavior of individual electrons in "ideal" crystals in the tight-binding model of solid state physics. Spectra of such operators have the usual band-gap structure, and the corresponding dispersion relations are algebraic varieties. In the 1990's Gieseker, Knorrer, and Trubowitz used toroidal compactifications to solve questions such as irreducibility of Bloch and Fermi varieties and the density of states, for a class of mono-atomic models. Their work showed that while spectral theory is focused on the real part of the Bloch variety, the study of complex singularities and compactifications is crucial for describing formation of bands and gaps. After a gap of 30 years, spectral theory is again interacting with algebraic geometry. Recently, W. Liu gave an algebraic method to obtain more general proofs of irreducibility for Fermi surfaces, Kravaris used free resolutions to study density of states, and Kuchment and coauthors used toric varieties and numerical nonlinear algebra to study spectral edges. These and other developments have led to the realization that many open questions in spectral theory may be studied using modern tools in algebraic geometry. These include the relation of reducibility/irreducibility with physical symmetries of the crystals, the structure of spectral band edges, and Dirac cones. These methods can also be applied to quantum graphs, such as graphene-type structures, and to obtain existence and non-existence theorems for embedded eigenvalues. The goal of this workshop is to bring together experts from spectral theory, mathematical physics, and algebraic geometry to understand, apply, and advance these new methods and interactions. A significant aspect of these reemerging interactions involves computation. A key recent development in algebraic geometry is computation, both symbolic and numerical. Computation and experimentation using tools from algebraic geometry have already been important in two recent papers by Sottile on this subject, and we expect it to become a useful tool for studying periodic operators. Speakers in this workshop are firmly rooted in the uses of computation and experimentation in applications of Algebraic Geometry, and many are familiar with exploiting the atmosphere and facilities of the ICERM to initiate collaboration.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Algebra,    Angewandte Mathematik (allgem.)

University of Pennsylvania

The Geometry and Strings 2023 conference is a continuation of the series of conferences that stem from the meetings "Physics and Geometry of F-theory", established in 2012. In 2019 the conference was renamed "Geometry and Strings 2019" in order to signify the broadening of the range of topics so as to attract a broader community with an interest in the interplay between geometry and string theory.

Mathematical Sciences Research Institute (MSRI)

The topical workshop will be dedicated to Shouwu Zhang, to mark the occasion of his 60th birthday, and to honour his numerous beautiful contributions to the theory of Shimura varieties and special values of L-functions. It will highlight cutting edge work on topics such as the construction of Euler systems; relations between special cycles on Shimura varieties and L-functions, such as generalized Gross-Zagier formulas and the Tate conjecture; the construction of Galois representations in cohomology; and related aspects of the theory of automorphic forms.

Northwestern University, Evanston, IL

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Recent developments in several disparate areas make it a pressing and opportune time to confront the interplay between topology, symmetry and interactions. This conference will catalyze the discussion on this broad topic by highlighting a burst of recent advancements, both theoretical and experimental, along this direction. An important goal is to enhance cross-talk between the weakly and strongly correlated communities interested in topology that have not yet had adequate interactions with each other. The conference will bring participants up to speed in this rapidly growing field and sharpen the central questions that will be discussed in the remainder of the associated program.

Festkörperphysik,    Mathematische Physik

UC Santa Barbara, Kavli Institute for Theoretical Physics (KITP)

Nanoparticle assembly is a hierarchical approach to functional materials. It operates at the mesoscale where elementary building blocks still feel their atomic nature and can profit from quantum function but at the same time are flexible enough in shape and interaction to permit high structural complexity. The realization of nanoparticle assemblies requires the convergence of and communication among several scientific disciplines: chemistry for synthesis, materials science for characterization, chemical engineering for up-scaling, and physics for a theoretical description and quantum phenomena. The goal of the conference will be to provide a coherent view of the current state of the field, bringing together researchers with different expertise and background. It should catalyze the development of new methods, both theoretical, computational and experimental, and define the basic science in this field. A focus will be recent developments but also a look forward: What should be the focus for the next decade and beyond? What are they key physics concepts that need to be developed and from where will the new game-changing technological advances emerge?

Clusterphysik, Nanowerkstoffe, Graphen und Fullerene,    Mathematische Physik

ICERM

This workshop focuses on the interplay between dynamics, rigidity, and arithmetic in hyperbolic geometry and related areas. There have been many striking developments in recent years, particularly related to totally geodesic submanifolds in both finite and infinite volume hyperbolic and even complex hyperbolic manifolds.

One aim of this workshop is to expose young researchers to these breakthroughs providing them with the necessary background from dynamics, and geometry to allow them to appreciate some of these recent advances, and prepare them to make new original contributions. For this purpose, we will have minicourses on ”Arithmeticity, Superrigidity and totally geodesic manifolds”, and ”Rigidity and geodesic planes in infinite volume hyperbolic manifolds”. These courses will be preceded by an introductory minicourse on Hyperbolic geometry. We will also have a minicourse on ”Understanding of geodesic planes in hyperbolic 3-manifolds via computations and visualization”. In addition, we wish to bring together experts in these fields to discuss the recent developments and open problems that lie at the crossroads of these different fields and to encourage more interaction among people working in these diverse areas.

Program Staff;     Tel.: [1-401-863-5030];     Email: info@icerm.brown.edu

ICERM

In spite of their omnipresence and importance, a number of questions about knots remain elusive. Addressing them solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology. Some of the most exciting recent avenues of research include optimizing geometry, quantum knot invariants, and applications in material sciences, physics, and molecular biology. This workshop emphasizes bridging the gap between theoretical, computational, and experimental approaches in knot theory and its applications, including artificial intelligence.

Program Staff;     Tel.: [1-401-863-5030];     Email: programstaff@icerm.brown.edu

Analysis,    Algebra

In the early 1920s, Emmy Noether introduced the fundamental concept of a Noetherian ring, a notion that has had a remarkably broad impact on mathematics over the last century. In this conference, we celebrate Noether's legacy with research talks from many areas of algebra, broadly construed, including algebraic geometry, commutative algebra, number theory, and representation theory.

Algebra,    Zahlentheorie, Arithmetik

Mathematical Sciences Research Institute (MSRI)

This graduate summer school will introduce students to two important and inter-related fields of differential geometry: geometric flows and minimal surfaces.

Kurse und Veranstaltungen für Studenten der Mathematik,    Algebra

Mathematical Sciences Research Institute (MSRI)

The school is built around two related courses on geometric (‘derived spaces’) and categorical (‘derived categories’) aspects of the theory. Our goal is to explain the key ideas and concepts, while trying to keep technicalities to a minimum.

ICERM

This will be a one-week conference broadly focused on the topics of the LMFDB, mathematical databases, computation, number theory, and arithmetic geometry. The conference will include invited talks, presentations by authors of papers submitted to the conference and selected by the scientific committee following peer-review, as well as time set aside for research and collaboration. This workshop is an activity of the Simons Collaboration 'Arithmetic Geometry, Number Theory, and Computation' and is supported by the Simons Foundation.

Program Staff;     Tel.: [1-401-863-5030];     Email: info@icerm.brown.edu

Zahlentheorie, Arithmetik,    Numerische Analysis

Kurse und Veranstaltungen für Studenten der Mathematik,    Algebra