Presentation The CRM and IMUB are pleased to announce the follow-up programme for the IRTATCA: Interactions between Representation Theory, Algebraic Topology and Commutative Algebra intensive research programme that was held in 2015 at the CRM. The program and its follow-up are devoted to promote interactions between researchers from different areas that share a common interest in homological techniques in a broad sense. The original programme gathered around 200 researchers from all over the world, and it is now time to have a look at some of the progress that took place since then.

These two weeks will be structured around one Advanced Course between the 3rd and 7th of June 2019, that will take place at the IMUB and a Conference between the 11th and the 15th of June 2019 that will take place at the CRM.​

Topics The programm is open to all researchers interested in homological algebra and its applications in areas like commutative algebra, representation theory and algebraic topology. This includes but is not restricted to: the study of triangulated categories, derived algebraic geometry, homotopy theory, singularity theory, representation theory, etc.

In recent years, several independent research groups have raised the possibility of a unified approach to the study of Khovanov-Rozansky knot homology, double affine Hecke algebras and elliptic Hall algebras, super Yang-Mills theory, Betti quantum geometric Langlands, and Hilbert schemes, seen through the lens of character varieties and related geometries. The aim of this workshop is to bring together researchers in topological field theory, geometric representation theory, mathematical physics, and algebraic combinatorics to report on recent progress and open questions at the intersection of these fields.

The conference will be preceded by a week-long summer school aimed at graduate and post-doctoral researchers, with the goal to initiate them to the ideas needed to follow the talks the following week. There will be an application process for this, and funding is available to cover the lodging for summer school participants for the duration of both events. We have addtional supplementary NSF funding for the travel costs of US-based summer school participants.

Summer school speakers:

Tina Kanstrup, Univeristy of Bonn

Pavel Safronov, University of Zurich

Hiro Lee Tanaka, Texas State University

Monica Vazirani, UC Davis

Conference speakers:

Mina Aganagic, UC Berkeley (*)

Adrien Brochier, University of Paris 7, Diderot

Ivan Cherednik, University of North Carolina

Tudor Dimofte, UC Davis

Pavel Etingof, MIT

John Francis, Northwestern University

Tamas Hausel, IST Vienna

Lotte Hollands, Heriot-Watt University

Anton Kapustin, Caltech

Anton Mellit, University of Vienna

Andrei Negut, MIT

Alexei Oblomkov, UMass Amherst

Tony Pantev, U Penn

Du Pei, Caltech

Pavel Safronov, University of Zurich

L. Schaposnik, University of Illinois, Chicago

Claudia Scheimbauer, NTNU Trondheim

Noah Snyder, Univeristy of Indiana, Bloomington

Constantin Teleman, UC Berkeley

Harold Williams, UC Davis

Dimitri Wyss, IST Vienna

(*) To be confirmed.

A website with up to date information is available at:

Conference: http://www.icms.org.uk/geometricrepresentation.php Summer school: http://www.icms.org.uk/GRTsummerschool.php

Applications for the summer school can be made from now until February 28th, 2019. Registration for the conference will begin January 15th, and run until February 28th; we'll send a reminder announcement at that time. Please feel free to email the organizers, at djordan@ed.ac.uk, in the meantime with any questions, or to let us know your intent to register.

For both events, the organizers are committed to a fair gender balance and to hosting a diverse body of participants. Members of under-represented groups are especially encouraged to apply to participate.

We hope to see you there, Dan Freed David Jordan Peter Samuelson Olivier Schiffmann

LG&TBQ is a conference aiming to to foster ongoing community and collaboration among LGBTQ+ mathematicians working in geometry, topology and dynamical systems. All are welcome.

The last 10 years have brought a burst of activity at the intersection of algebraic topology, number theory and algebraic geometry. This has led to a wealth of: New theorems, such as Ellenberg–Venkatesh–Westerland’s breakthrough results on the Cohen–Lenstra heuristics for function fields; New sources of heuristics in topology, such as Vakil–Wood’s predictions from the Grothendieck ring, or the notion and coincidences of homological densities as in Farb– Wolfson–Wood; Refinements of classical enumerative theorems using modern topological tools, such as Kass–Wickelgren’s arithmetic count of the 27 lines on a cubic surface; and A renewed focus on unstable homology, as in Galatius–Kupers–Randal-Williams and Miller–Wilson. We believe that these results are just the beginning of the emerging area of arithmetic topology.

This 5 day workshop will bring together junior and senior researchers from across these areas with the goal of:

Giving participants a global view of a fast emerging and multidisciplinary area,
Giving participants a detailed awareness on the range of methods available, and
Emerging with a robust problem list which can help guide activity in the area for the next 5-10 years.

We would like to announce a two week program on Low-dimensional topology, geometry, and applications to be held at the IMA (Minnesota) in June 2019. In the first week (17 – 22 June), we will run a summer school targeted at (but not restricted to) PhD students and postdocs. There will be four courses given by

• Jun O'Hara (Chiba, harmonic analysis)
• Peter Schröder (Caltech, discrete differential geometry)
• Jennifer Schultens (UC Davis, 3-manifolds)
• Gert van der Heijden (UC London, nonlinear mechanics)

as well as a special lecture by Ken Millett (UCSB, microbiology).

In the second week (24 – 28 June) there will be a workshop providing a platform to present the most recent developments in the fields presented at the summer school.

Please register at the IMA website. Limited travel support for young participants may be available.

The organizing committee: Simon Blatt, Elizabeth Denne, Philipp Reiter, Armin Schikorra

IMA Minnesota 207 Church Street SE Minneapolis, MN 55455 United States

More information: https://www.ima.umn.edu/2018-2019/SW6.17-28.19

The center for Symmetry and Deformation is celebrating its 10 years anniversary with a conference. More info can be found on the webpage.

The fifth European Talbot workshop will take place in Germany July 7 - 13, 2019. The goal is to bring together a group of 30-35 graduate students and post-docs to work on a focused topic, this year algebraic K-theory, under the guidance of two senior mentors.

Most of the talks were given by the participants, with enough free time in the afternoon and evenings for further discussions and interaction. The character of the workshop is expository in nature, starting with the basic ideas and leading to a survey of the most recent developments in the field. Since all participants are staying together at a group house, jointly responsible for cooking and cleaning, we hope to create an informal and inspiring atmosphere.

An informal workshop focusing on the interactions between the cohomology, homotopy, and p-local theory of finite groups of Lie type, p-compact groups, and the free loop spaces of classifying spaces of p-compact groups.

This workshop will bring together researchers from the worlds of low- and high-dimensional manifold topology, especially those with interests in the study of 4-manifolds.

Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology Workshop (WiSCon)

July 22 - 26, 2019

ICERM, Brown University

WiSCon is a Research Collaboration Conference for Women (RCCW) in the fields of contact and symplectic geometry/topology and related areas of low-dimensional topology. The goal of this workshop is to bring together women and nonbinary researchers at various career stages in these mathematical areas to collaborate in groups on projects designed and led by female leaders in the field.

Senior graduate students and early career researchers (including tenure-track) are strongly encouraged to apply!

Participants will work in teams on research projects, with researchers leading the projects including: • Penka Georgieva (Sorbonne) • Eli Grigsby (Boston College) • Tara Holm (Cornell) • Jen Hom (Georgia Tech) • Ailsa Keating (Cambridge) • Christine Ruey Shan Lee (University of South Alabama) • Chiu-Chu Melissa Liu (Columbia) • Allison Moore (UC Davis) • Emmy Murphy (Northwestern) • Yu Pan (MIT) • Ina Petkova (Dartmouth) • Ana Rita Pires (Edinburgh) • Olga Plamenevskaya (Stony Brook) • Radmila Sazdanović (North Carolina State) • Laura Starkston (UC Davis) • Lisa Traynor (Bryn Mawr) • Vera Vértesi (Strasbourg) • Katrin Wehrheim (UC Berkeley)

Applications are now open and will close on December 3, 2018.

This workshop is partially supported by NSF-HRD 1500481 - AWM ADVANCE grant.

Young Topologists Meeting 2019 will be held from Monday, July 22, to Friday, July 26, 2019 at EPFL in Lausanne, Switzerland.

The conference is intended as an opportunity for graduate students, recent PhDs, and other junior researchers in topology (both pure and applied) to meet each other and share their work. In addition to short talks by participants, the program for the meeting will include two lecture series by:

• Julie Bergner (University of Virginia)
• Vidit Nanda (University of Oxford)

Further information is going to be made available on the conference website at ytm2019.epfl.ch. The organizers can be contacted at ytm2019@epfl.ch.

A Jolly Pleasant Conference for Greenlees (J.P.C. Greenlees) officially known as Equivariant Topology and Derived Algebra

A conference in honour of John’s 60th birthday

The purpose of the workshop is to support and expand research efforts by female mathematicians in the field of algebraic topology. The workshop will bring senior and junior researchers together with advanced graduate students to cooperate on research projects on topics of common interest. The focus of the workshop will be on active collaboration to advance the projects, rather than on knowledge communication through lectures.

An autumn school on computations in motivic homotopy theory with lecture series by Marc Hoyois, Oliver Röndigs, Kirsten Wickelgren, and Paul Arne Østvær. Please register at the school's website. Limited financial support is available.

We organize an Oberwolfach Seminar on Topological Cyclic Homology and Arithmetic. The purpose of the seminar is to introduce the higher algebra refinements of determinant and trace, namely, algebraic K-theory and topological cyclic homology, along with their budding applications in arithmetic geometry and number theory. In particular, we will use these ingredients to build Clausen's Artin map from K-theory of locally compact topological R-modules to the dual of his Selmer K-theory of R, and explain that for R a finite, local, or global field, this implies Artin reciprocity. If you wish to participate, please follow the instructions described here to register at ag@mfo.de by August 11, 2019.

The Banff International Research Station will host the "Equivariant Stable Homotopy Theory and p-adic Hodge Theory" workshop in Banff from March 1 to March 06, 2020.

Algebraic topology has had a long and fruitful collaboration with algebraic geometry, with each providing techniques and problems to the other. This workshop is aimed at an exciting, evolving incarnation of this story: applications of equivariant stable homotopy to number theory. Recent work on the foundations of equivariant stable homotopy theory (starting with the Hill--Hopkins--Ravenel work on the Kervaire invariant one problem) and Lurie's development of the foundations of ''derived algebraic geometry'' now allows systematic exploration and organization of ''equivariant derived algebraic geometry''. This allows us to do ordinary algebraic geometry in commutative ring spectra.

New foundations in this area have been spectacularly applied to phenomena seen in the trace methods approach to computing algebraic K -theory. For instance, although the theory of equivariant commutative ring spectra was described decades ago, few of the subtleties in the theory were understood or explored. The modern approaches to computing algebraic K-groups step through equivariant commutative ring spectra via the natural S1-action on topological Hochschild homology. Ongoing and transformative work by Bhatt--Morrow-Scholze in p-adic Hodge theory uses cyclotomic spectra and therefore subtle equivariant information. This workshop, at the vanguard of work in this area, seeks to bring together experts in algebraic topology, (derived) algebraic geometry, and number theory to explore these exciting new connections.

See conference website