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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

Workshop on Interactions between Dynamical Systems and Partial Differential Equations (JISD 2014)

The twelfth edition of the WORKSHOP ON INTERACTIONS BETWEEN DYNAMICAL SYSTEMS AND PARTIAL DIFFERENTIAL EQUATIONS (JISD2014) will be held in Barcelona, June 16 – 20, 2014, at the Universitat Politècnica de Catalunya (UPC)

There will be four main courses of six hours each, some seminars, communications, and posters. The courses will be taught within the Master of Science in Advanced Mathematics and Mathematical Engineering (MAMME) of the UPC Graduate School.

Courses taught by:

– Alessio Figalli (Univ. of Texas Austin)
– Konstantin Khanin (Univ. of Toronto) 
– Sylvia Serfaty (Université Pierre et Marie Curie Paris 6) 
– Susanna Terracini (Università di Torino)

One hour seminars by:

– Scott Armstrong (Université Paris Dauphine): “Quantitative stochastic homogenization of convex energy functionals” 
– Gianmaria Verzini (Politecnico di Milano): “Strong competition versus fractional diffusion”

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Venue: Universitat Politècnica de Catalunya

Rational and Integral Points on Higher-dimensional Varieties

The goal of this workshop is to bring together researchers in algebraic geometry, cohomological methods, and analytic methods to study connections between these perspectives in Diophantine geometry.

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Venue: American Institute of Mathematics

Women in Numbers 3

The workshop aims to promote research and leadership among female number theorists within a supportive environment.

Number theory has its roots in the study of the integers, but the great variety of tools and techniques motivated by these ancient questions are now allowing us to address questions intimately connected to a wide variety of fields, from geometry to physics and information theory. This workshop is a continuation of the previous two successful BIRS workshops for women in numbers. It will bring together women at all stages in their research careers, from senior faculty to graduate students, to do new research in some of the most important and vibrant areas of modern number theory, and to continue to build a thriving community of women working in the area.

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Venue: BIRS

Representation Theory Days in Patagonia

A focused workshop on recent research in geometric representation theory and related physics.

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Venue: Punta Arenas, Chile

Moduli Spaces in Geometry

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Venue: CIRM, Luminy

Deformation Theory, Completed Cohomology, Leopoldt Conjecture and K-theory

There has been exciting progress recently on two (three ?) connected topics: the extension of the Taylor-Wiles method to situations where the standard (im)parity condition fails, and the relation of deformation theory (starting with Hida’s idea) with the Leopoldt conjecture. The salient points are the paper(s) of Calegari and Geraghty, Calegari’s paper on stable (completed) homology for congruence groups, and the Khare-Thorne paper on Leopoldt; the construction of new Galois representations by Harris-Lan-Thorne-Taylor and Scholze, in particular for torsion classes, is also a crucial advance. Finally, Calegari’s paper reveals new relations with problems in K-theory on which our kowledge does not seem to have improved much since the Batelle meetings.

This workshop will be limited to the researchers involved in these developments. The aim is to obtain an up-to date integrated picture of these developments as well as their interrelations.  Connected theories such as completed cohomology should be reviewed, as well as some complements in K-theory. 

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Venue: CIRM, Marseille

Amenability, Coarse Embeddability and Fixed Point Properties

The main theme of the workshop is the spectrum of analytic properties running from Kazhdan’s property (T) at one end to von Neumann’s amenability at the other, that forms a foundational organizing structure for infinite groups and spaces. These properties can be described both analytically, via unitary representation theory, and geometrically, using embedding properties for discrete spaces. Connections with probability and combinatorics will likewise be addressed during the meeting.

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Venue: MSRI

Geometric Group Theory and Low-Dimensional Topology

This advanced school and workshop will focus on themes at the cutting edge of research in geometry and topology and its connections with group theory.  It will expose students, post docs, and researchers to various key roles that geometric group theory has played in recent advances in low-dimensional topology and geometry.  These include, but are not limited to, the role of virtually special groups, representations of Kleinian groups in SL(2,C) and generalizations (e.g. Higher Teichmüller Theory), the mapping class group and its recent role in low dimensional geometry and topology and group theory connections with Heegaard Floer theory through left-orderability.

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Venue: Abdus Salam International Centre for Theoretical Physics, Trieste, Italy