Meetings/Workshops on Algebra in the United States (USA)

Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating non-generic geometric situations (such as non-transverse intersections in intersection theory), in lieu of the more traditional perturbative approaches (such as the "moving" lemma). This direct approach, in addition to being conceptually satisfying, has the distinct advantage of preserving the symmetries of the situation, which makes it much more applicable. In particular, in recent years, such techniques have found applications in diverse areas of mathematics, ranging from arithmetic geometry, mathematical physics, geometric representation theory, and homotopy theory. This semester long program will be dedicated to exploring these directions further, and finding new connections.

Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. In this program we aim to bring together key researchers in these and related areas to highlight the recent exciting progress and to explore future avenues of research. This program will focus on the following themes: Geometry and Derived Categories, Birational Algebraic Geometry, Moduli Spaces of Stable Varieties, Geometry in Characteristic p>0, and Applications of Algebraic Geometry: Elliptic Fibrations of Calabi-Yau Varieties in Geometry, Arithmetic and the Physics of String Theory.

The conference will feature a series of ten lectures by Professor Kannan Soundararajan from Stanford University who is well known for his prolific and influential research in this area, and also for his skill as a lecturer and expositor. Number theory is an old and very active branch of mathematics, and the theory of L-functions has played a central role in its modern development. The tools used to study L-functions draw from many fields including analysis, algebra, algebraic geometry, automorphic forms and representation theory, probability and random matrices, and even mathematical physics. The broad theme for the conference will be the value distribution of zeta and L-functions. The lecture series will touch upon several important questions including the maximal size of L-functions, asymptotics for moments of L-values, the distribution of zeros, and non-vanishing of L-functions at special points.

Professor Alain Miranville of the University of Poitiers (France) will deliver the main lecture series. Professor Miranville is an international expert in CH-type equations and applications and a world renowned expositor and lecturer. Miranville's ten lectures will take the participants on a journey through the subject beginning with the derivation of the equation and associated boundary conditions, through the analysis of the problems, numerical methods, and ending with cutting edge applications of Cahn-Hilliard (CH) type equations in fluid dynamics, image inpainting, and tumor growth. The proposed lectures and panel discussions heavily emphasize open research problems across multiple scientific fields. The discovery that tumor growth can be effectively modeled using CH-type equations is recent and holds great promise. Applications in fluid dynamics and inpainting are equally promising and will be presented.

The school is aimed to educate graduate students and young researchers in recent trends around Integrable Probability - a rapidly developing field at the interface of probability / mathematical physics / statistical physics on the one hand, and representation theory / integrable systems on the other. There will be 4 mini-courses: Week 1 - Dmitry Chelkak (École Normale Sup?rieure, Paris, France) - Ole Warnaar (University of Queensland, Brisbane, Australia) Week 2 - Tomohiro Sasamoto (Tokyo Institute of Technology, Tokyo, Japan) - Paul Zinn-Justin (University of Melbourne, Melbourne, Australia)

The fifth meeting of the Temple University Graduate Student Conference in Algebra, Geometry, & Topology will take place in Philadelphia, PA from June 1-2, 2019. Past conferences have had over 100 graduate students in attendance. Our goal is to expose graduate students to cutting edge research highlighting the beautiful and fruitful interactions between algebra, geometry, and topology. Additionally, this conference provides a forum for more senior students in these areas to both present their work and form research connections both within and across fields.

Courses and Events for Math Students and Early Career Researchers,    Geometry and Topology

This workshop, sponsored by AIM and the NSF, will be devoted to the study of smooth concordance classes of topologically slice knots.

Conference topics will include Groebner bases, toric varieties, Cox rings, syzygies, and applications to CAD software.

American Mathematical Society

The aim of this conference is to identify and prioritize future work in algebraic combinatorics and its related fields, including symmetric function theory, representation theory, and many other areas. Adriano Garsia's contribution to the field is as fundamental as legendary and we will happily used this opportunity to celebrate his 90th birthday.

This workshop, sponsored by AIM and the NSF, will be devoted to identifying and attacking "hot" open problems in the spectral shape optimization characterized by an interplay between the geometry and singularly supported potentials.

This summer school will give an introduction to representation stability, the study of algebraic structural properties and stability phenomena exhibited by sequences of representations of finite or classical groups -- including sequences arising in connection to hyperplane arrangements, configuration spaces, mapping class groups, arithmetic groups, classical representation theory, Deligne categories, and twisted commutative algebras. 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.

Courses and Events for Math Students and Early Career Researchers,    Group Theory

The Mathematics Academy is a unique opportunity for students interested in examining mathematical concepts rarely offered at the high school level. This rigorous, proof-oriented program will fuse lectures, problem sessions, demonstrations, and exploratory research to engage students.

Discrete Mathematics, Algebra and Number Theory, Geometry and Topology

Courses and Events for Math Students and Early Career Researchers,    Geometry and Topology

This workshop, sponsored by AIM and the NSF, will address questions of existence and uniqueness of equilibrium states, and their statistical properties, for dynamical systems arising from geometry, particularly geodesic flows.

This workshop, sponsored by AIM and the NSF, will be devoted to the zero distribution of random polynomials spanned by various deterministic bases.

The Illustrating Mathematics program brings together mathematicians, makers, and artists who share a common interest in illustrating mathematical ideas via computational tools. The goals of the program are to: introduce mathematicians to new computational illustration tools to guide and inform their research; spark collaborations among and between mathematicians, makers and artists; and find ways to communicate research mathematics to as wide an audience as possible.

Geometry and Topology, Algebra and Number Theory, Dynamics and Probability,

Geometry and Topology,    Number Theory, Arithmetic

This workshop, sponsored by AIM and the NSF, is devoted to the working on the birational classification of noncommutative surfaces and related problems. The goal is that these related results would deal with important cases in Artin's conjectured classification and make progress towards an ultimate classification.

Mathematical Sciences Research Institute (MSRI), Berkeley

Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

Mathematical Sciences Research Institute (MRSI)

This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic K-theory. These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace.