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.

There will be about 15 mini-courses of introductory nature, related to the Geometry-Topology research subjects. Graduate students, recent Ph.D.s and under-represented minorities are especially encouraged to the summer school. Partial financial support is available.

The annual British Topology Meeting will this year be held at the University of Warwick. Speakers include:

• Keiran Fleming (University of Leicester)
• Jelena Grbic (University of Southampton)
• Lennart Meier (University of Utrecht)
• Luca Pol (University of Sheffield)
• Constanze Roitzheim (University of Kent)
• Bernadette Stolz (University of Oxford)
• James Walton (University of Glasgow)
• Ittay Weiss (University of Portsmouth)
• Ana Garcia-Pulido (University of Liverpool)

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.

he workshop Women in Geometry and Topology is an endeavour organized by the GEOMVAP research group at UPC and financed under the AGAUR project 2017SGR932.

The group GEOMVAP focuses in Geometry and Topology in the broad sense and its applications to several topics suchs as Celestial Mechanics, Control Theory, Mathematical Physics, Phylogenetics and Robotics. GEOMVAP promotes, in particular, Responsible, Research and Innovation within the framework of Horizon 2020. Among the RRI initiatives we strive for gender equality, public engagement, science communication and the visibility of women in Science and Society.

The Workshop Women in Geometry and Topology will feature several plenary talks by top female mathematicians and some contributed talks (contributed by speakers of any gender identity).

There will be two public lectures by Marta Macho (Scientific Culture Chair UPV/EHU, RSME Medal 2015, Emakunde Equality Prize 2016) and Carme Torras (Narcís Monturiol Medal 2000) addressed to the general public (you don't need to be a mathematician to follow them you just need to be curious!). A panel (open to the public) will also be organized in order to discuss the situation of women in mathematics, the gender gap and strategies for breaking the glass-ceiling inside and outside academia. Other complementary activities will be announced in due time.

The publication of "extended abstracts" from the congress is expected in the prestigious Springer-Birkhäuser Research Perspectives CRM Barcelona collection, within the Trends in Mathematics series.

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.

Arithmetic groups provide a fruitful link between various areas, such as geometry, topology, representation theory and number theory. Methods from geometry and topology hinge on the fact that arithmetic groups are lattices in Lie groups, whereas the theory of automorphic forms establishes a connection to representation theory and number theory. This interplay is especially intriguing in the setting of hyperbolic 3-manifolds. Indeed many conjectures in 3-manifold theory tend to be much more accessible for hyperbolic 3-manifolds whose fundamental groups are arithmetic, and conversely such manifolds provide the simplest set-up in which some of the most exciting new phenomena in the Langlands program can be studied. This conference will bring together researchers with various backgrounds around links between number theory and 3-manifolds. Central topics of the conference are the cohomology of arithmetic groups, the relation between torsion and L²-torsion, profinite invariants of 3-manifolds, and number theoretic ramifications.

Andrew Ranicki and his theory of algebraic surgery played a central role in linking manifold theory, algebraic K-theory, and its close cousin L-theory. These areas have seen great developments and advances in the last decade from distinct research communities. This workshop will bring together mathematicians working on the topology of high-dimensional manifolds and their automorphisms with those working on the algebraic K-theory (and its cousins hermitian K-theory and L-theory) of rings and ring spectra, in order to share recent progress in these areas and kindle a fresh interaction between them.

See conference website

The goal of this summer school is to introduce participants to modern tools used in the study of fixed point theory in algebraic topology and homotopy theory. The workshop will be centered around mini-courses whose goal will be to introduce and apply tools such as categorical approaches to duality, spectra and trace methods in algebraic K-theory to the study of classical fixed point theory.

The intended audience for this summer school should be familiar with the material in Hatcher (except the appendices). This reflects our goal that the school be accessible to second and third year students with an interest in algebraic topology from any PhD granting institution. The school will be structured around a few mini-courses which will run in an active-learning style.

Scientific Leaders

Jonathan Campbell, Vanderbilt University

Inbar Klang, École Polytechnique Fédérale de Lausanne

Kate Ponto, University of Kentucky

Cary Malkiewich, Binghamton University

John Lind, California State Chico

Sarah Yeakel, University of Maryland

Inna Zakharevich, Cornell University