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Springer, [Cham]. Quanta Magazine. Natalie Wolchover. March 28, Retrieved May 2, Contemporary Mathematics.

Proceedings of the London Mathematical Society. Current Developments in Mathematics.

Covering spaces and 2-oriented graphs - Algebraic Topology - NJ Wildberger

The Jerusalem Post. The conjecture was finally given an exceptionally elegant proof by A. Marcus and G. Tardos in Working with Ben Green, he proved there are arbitrarily long arithmetic progressions of prime numbers—a result now known as the Green—Tao theorem. Discrete Mathematics. Mathematics of Computation.

Croot, Ernest S. Inventiones Mathematicae. From the reviews: "This is an introduction to the beautiful world of combinatorial algebraic topology, describing the modern research tools and latest applications in this field. Added to basket. Bibcode : math Classification theory for abstract elementary classes. College Publications. July 24, Categoricity PDF. American Mathematical Society.

Previous Seminars - 2011 to 2012

Archived PDF from the original on July 29, Retrieved February 20, Bibcode : arXiv Journal of Symbolic Logic. May Journal of Combinatorial Theory, Series B. Foreman, Banff, Alberta, Die Welt der Primzahlen. Springer-Lehrbuch in German 2nd ed. June Notre Dame Journal of Formal Logic. See in particular p. Bibcode : Natur. In Creignou, N. Lecture Notes in Computer Science. Springer, [Cham].

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Communications in Algebra. Research in the Mathematical Sciences. Quanta Magazine. Natalie Wolchover. March 28, Archived from the original on April 24, Retrieved May 2, Contemporary Mathematics. Retrieved 24 April Society for Industrial and Applied Mathematics. Archived PDF from the original on 23 October Acta Mathematica.

Documenta Mathematica. The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow. In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques.

In this summer school, we will discuss these new techniques as well as some exciting recent developments. Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject.

Geometric group theory studies discrete groups by understanding the connections between algebraic properties of these groups and topological and geometric properties of the spaces on which they act. The school will also include students presentations to give the participants an opportunity to practice their speaking skills in mathematics.

Finally, we hope that this meeting will help connect Latin American students with their American and Canadian counterparts in an environment that encourages discussion and collaboration.

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Representation stability incorporates tools from commutative algebra, category theory, representation theory, algebraic combinatorics, algebraic geometry, and algebraic topology. This workshop will assume minimal prerequisites, and students in varied disciplines are encouraged to apply. The study of locally symmetric manifolds, such as closed hyperbolic manifolds, involves geometry of the corresponding symmetric space, topology of towers of its finite covers, and number-theoretic aspects that are relevant to possible constructions.

The workshop will provide an introduction to these and closely related topics such as lattices, invariant random subgroups, and homological methods.

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Linkage is a method for classifying ideals in local rings. Residual intersections are ubiquitous: they play an important role in the study of blowups, branch and multiple point loci, secant varieties, and Gauss images; they appear naturally in intersection theory; and they have close connections with integral closures of ideals. The theory of tight closure and test ideals has widespread applications to the study of symbolic powers and to Briancon-Skoda type theorems for equi-characteristic rings.

Numerical conditions for the integral dependence of ideals and modules have a wealth of applications, not the least of which is in equisingularity theory. The Rees ring and the special fiber ring of an ideal arise in the process of blowing up a variety along a subvariety. Rees rings and special fiber rings also describe, respectively, the graphs and the images of rational maps between projective spaces. A difficult open problem in commutative algebra, algebraic geometry, elimination theory, and geometric modeling is to determine explicitly the equations defining graphs and images of rational maps.

The school will consist of the following four courses with exercise sessions plus a Macaulay2 workshop. 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. 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. Harmonic analysis is a central field of mathematics with a number of applications to geometry, partial differential equations, probability, and number theory, as well as physics, biology, and engineering. The Graduate Summer School will feature mini-courses in geometric measure theory, homogenization, localization, free boundary problems, and partial differential equations as they apply to questions in or draw techniques from harmonic analysis.

The goal of the program is to bring together students and researchers at all levels interested in these areas to share exciting recent developments in these subjects, stimulate further interactions, and inspire the new generation to pursue research in harmonic analysis and its applications. After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, and foliation theory.

Jointly hosted by Janelia and the Mathematical Sciences Research Institute MSRI , this program will bring together advanced PhD students with complementary expertise who are interested in working at the interface of mathematics and biology.

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Emphasis will be placed on linking behavior to neural dynamics and exploring the coupling between these processes and the natural sensory environment of the organism. The aim is to educate a new type of global scientist that will work collaboratively in tackling complex problems in cellular, circuit and behavioral biology by combining experimental and computational techniques with rigorous mathematics and physics.

Higher categorical structures and homotopy methods have made significant influence on geometry in recent years. This summer school is aimed at transferring these ideas and fundamental technical tools to the next generation of mathematicians. The prerequisites will be kept at a minimum, however, a introductory courses in differential geometry, algebraic topology and abstract algebra are recommended.

The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Two central themes will be those of partial hyperbolicity on one side, and rigidity, group actions and renormalization on the other side. We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra.

We will give a comprehensive introduction to the "tool box" of modern higher representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory. Subfactor theory is a subject from operator algebras, with many surprising connections to other areas of mathematics.