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Exterior Differential Systems and Lie Theory

This workshop will bring together mathematicians working in two different, but related, fields: Exterior Differential Systems and Cartan’s Equivalence Method on the one hand and Lie theory (especially Lie pseudo-groups and Lie groupoids/algebroids) on the other. Not only there have been some very exciting advances in these subjects recently, but also it has became clear in the last few years that these areas are intimately connected. Hence, given the current interest by different groups of people and different viewpoints, there is a need for a focused workshop which can bring together the top researchers, promising young researchers, and students in these very active fields.  

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Venue: Fields Institute

Women in Numbers Europe

The workshop will have the dual objectives of carrying out simultaneous research projects during the conference that result in on-going collaborations and mentoring junior women in mathematics. The conference will bring together established researchers, young faculty, and advanced graduate students. 

The conference will highlight and advance the scientific goals and research agendas of women who are active and successful researchers in number theory. At the same time this framework will be used to help create a strong collaboration network for young female researchers coming into the field, connect them with important research directions and expand their network of collaborators and research mentors. 

Rather than focusing on disseminating the results of established researchers, the workshop will focus on research projects that will be started during the week of the workshop and have the potential to result in on-going collaboration between the participants.

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Venue: CIRM, Luminy

Women in Topology

Homotopy theory is a very active field of modern mathematics, which not only has contributed  significantly to many other fields of mathematics and theoretical physics but is also now being applied to problems in engineering and computer science. As in any other fields of mathematics research, women are underrepresented in homotopy theory. In recent years, however, there has been a small but steady increase in the number of female researchers in the field. This workshop aims to capitalize on this trend, by bringing senior and junior researchers together with graduate students to work on open problems, thus providing a context for collaborations and establishing networks for future research. The ultimate goal is to increase the number and visibility of active female researchers in homotopy 
theory.

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Venue: Banff International Research Station,

Ricci Curvature: Limit Spaces and Kähler Geometry

This ICMS program consists of a one-week summer school followed by a one-week workshop. The summer school will introduce PhD students and other early-career researchers to essential topics necessary for an understanding of contemporary developments in the field — most spectacularly perhaps, the recent resolution of the existence of Kähler-Einstein metrics on Fano manifolds announced by Donaldson and coworkers and by Tian in December 2012. Work in this area is highly technical and demands background in several areas; few early-career researchers have this breadth of background and therefore for most early-career researchers attendance at the summer school is an integral part of the preparation for the workshop. The five summer school courses have been specially designed to prepare participants for the advanced mini-series of lectures which form the core of the workshop in week 2 and which will present the latest results of research in this area including the work onKähler-Einstein Fano problem.

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Venue: ICMS, Edinburgh

Multiple Zeta Values, Modular Forms and Elliptic Motives II

Speakers: C. Bogner (Berlin), D. Broadhurst (Open University), F. Brunault (ENS Lyon), B. Enriquez (CNRS), G. Felder (ETH Zürich), R. Friedrich (MPIM Bonn), Y. Iijima (RIMS), M. Kaneko (Kyushu), M. Kim (Oxford), U. Kühn (Hamburg), M. Levine (Duisburg-Essen), Y. Manin (MPIM Bonn), H. Nakamura (Osaka), A. Salerno (Bates), L. Schneps (CNRS), S. Stieberger (MPI Physik). T. Terasoma (Tokyo), P. Vanhove (IHES), K. Vogtmann (Cornell and Warwick), S. Wewers (Ulm)

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Venue: ICMAT, Madrid

Automorphic Forms, Shimura Varieties, Galois Representations and L-functions

L-functions attached to Galois representations coming from algebraic   geometry contain subtle arithmetic information (conjectures of Birch and Swinnerton-Dyer, Deligne, Beilinson, Bloch and Kato, Fontaine and Perrin-Riou). Langlands has predicted the existence of a correspondence relating these L-functions to L-functions of automorphic forms which are much better understood. The workshop will focus on recent developments related to Langlands correspondence (construction of Galois representations attached to automorphic forms via the cohomology of Shimura varieties, modularity of Galois representations…) and arithmetic of special values of L-functions.

It will be dedicated to Michael Harris as a tribute to his enormous influence on the themes of the workshop.

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Venue: MSRI

Categorical Structures in Harmonic Analysis

The workshop will focus on the role of categorical structures in number theory and harmonic analysis, with an emphasis on the setting of the Langlands program. Celebrated examples of this theme range from Lusztig’s character sheaves to Ngo’s proof of the Fundamental Lemma. The workshop will be a forum for researchers from a diverse collection of fields to compare problems and strategies for solutions.

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Venue: MSRI

Homotopy Type Theory

Homotopy type theory (HoTT) is a new and exciting approach to the foundations of mathematics. This workshop will bring together type theorists and homotopy theorists. The aim of the workshop is to develop an understanding of the possible applications of HoTT (and similar systems) to homotopy theory, and to discuss what is required from a foundational system for it to be convenient for homotopical mathematics.

Speakers:  Samson Abramsky, Benedikt Aherns, Thorsten Altenkirch, Andrej Bauer, Guillaume Brunerie, John Cartmell, Thierry Coquand, James Cranch, Daniel R. Grayson, Robert Harper,Martin Hyland, Chris Kapulkin, Dan Licata, Peter LeFanu Lumsdaine, Ieke Moerdijk, Egbert Rijke, Neil Strickland, Vladimir Voevodsky

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Venue: University of Oxford

New Geometric Structures in Scattering Amplitudes

Recently, remarkable mathematical structures have emerged in the study of scattering amplitudes, revealing deep links to algebraic geometry, arithmetic and combinatorics. There have been many exciting dual representations of amplitudes including

  • polytopes, twistor diagrams and the positive grassmannian leading to the concept of the `amplituhedron’,
  • polylogs, multizeta values and multiloop integrals,
  • Wilson loops and correlation functions, leading to hidden symmetries and integrability,
  • holomorphic strings in twistor and ambitwistor spaces,
  • asymptopia, holography and the BMS group.

Each of these disparate ideas and methods have their own remarkable successes, and indeed have led to important progress in related areas of mathematics. They also face obstacles that they need to overcome in order to become important tools in resolving the most important open conjectures in the field and for the explicit construction of amplitudes.  This workshop will bring together experts in the various strands in order to establish and consolidate their connections, to overcome the various obstacles. This will also be an opportunity to celebrate the work of Andrew Hodges on his 65th birthday.

Speakers: Nima Arkani-Hamed, Nathan Berkovits, Francis Brown, Freddy Cachazo, James Drummond, Michael Green, Paul Heslop, Andrew Hodges, Marcus Spradlin, Andy Strominger, Anastasia Volovich, Pedro Vieira, Pierre Vanhove, Lauren Williams.

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Venue: University of Oxford

Building Bridges: 2nd EU/US Workshop on Automorphic Forms and Related Topics

The workshop, partially funded by the Heilbronn Institute for Mathematical Research, aims to foster and strengthen a long-lasting exchange between automorphic forms researchers in the EU and the US. Based on the long-standing annual Workshop on Automorphic Forms and Related Topics, this workshop also aims to generate and sustain a friendly, supportive atmosphere, providing encouragement to young researchers, mentoring opportunities for more established researchers, as well as a forum for exchanging ideas and forming new collaborations.

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Venue: Bristol University

Symmetries and Correspondences in Number Theory, Geometry, Algebra and Quantum Computing

Symmetries and correspondences play the most central role in modern number theory. Class field theory and Langlands type correspondences are complemented by other powerful theories such as arithmetic noncommutative class field theories, a variety of higher class field theories, insights from anabelian geometry, mean-periodicity correspondence for zeta functions of arithmetic schemes. Recent work in arithmetic, functional, geometric Langlands correspondences, noncommutative summation formulas, new developments in anabelian geometry, higher adeles and zeta integrals for arithmetic schemes, dualities on arithmetic surfaces, higher equivariant Riemann–Roch theorems, higher commutative summation formulas, as well as related work in representation theory, algebraic analysis, geometry, K-theory, archimedean L-functions and integrable systems, the study of interaction with mirror symmetry, TQFT and quantum computation reveal new intra-disciplinary fundamental structures and stunning perspectives. Several of the new structures are higher structures in the sense of their level of complexity and their relation with higher structures in geometry, topology and category theory.

Talks will be given by leaders in their areas. They will often be of less technical and more general, overview and programme nature, describing new trends and perspectives and sketching potential for developments and interaction with other areas of mathematics.

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Venue: University of Oxford

Groups, Numbers and Dynamics Workshop

The aim of this workshop is to bring together researchers working in number theory, group theory and the theory of dynamical systems to discuss problems arising at the interface of arithmetics and dynamics of group actions. In recent years several promising connections between these fields has been discovered that resulted in striking breakthroughs.

Among the areas addressed during the workshop will be in particular connections between dynamics on homogeneous spaces and Diophantine geometry; exponential sums, dynamics on nilmanifolds and higher order correlations; periodic orbits, period integrals and L-functions including connections with quantum chaos.

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Venue: Isaac Newton Institute