Part of the Semester Program "Homotopy Harnessing Higher Structures." This programme will highlight four related themes: the new algebraic topology of differentiable manifolds, derived representation theory and equivariant homotopy theory, the interplay between arithmetic geometry and stable homotopy theory, and the analysis of foundations in these new contexts "the homotopy theory of homotopy theory". This workshop will focus on the algebraic topology of manifolds.

FRG-supported conference on the interaction between symplectic topology and homotopy theory.

The last four decades have revealed many deep connections between topological quantum field theory (TQFT), low-dimensional topology, and geometric structures on manifolds, particularly hyperbolic geometry. This conference will further explore and strengthen these connections by bringing together a distinguished international group of researchers working in or at the interface of these subjects.

Categorification is a flexible and powerful set of techniques and ideas, which produces insight about mathematical structures by viewing them as shadows of objects in a richer world, often described in terms of higher categories. Two important and interrelated categorification programmes, which are the basis for this workshop, concern the concepts of quantum link homologies and higher representation theory. Both have their origin in mathematics, but have since developed into some of the most fruitful grounds for collaboration between pure mathematics and theoretical physics.

The first week of this workshop will make the recent rapid developments in the areas of quantum link homologies and higher representation theory accessible to non-experts and intensify communication between specialists in these and related areas like gauge theory, TQFT, quantum Teichmüller theory, and string theory. The second week will be used to host a research conference with thematic emphasis on categorification of skein theory and 3-manifold invariants.

This meeting will bring together students, postdocs, and researchers from all over the world to stimulate research on fundamental questions in manifold theory. It will promote the interaction between researchers in high and low dimensional topology. The meeting is structured as follows: mini-courses in the first week by world experts (Lueck, Stipsicz, and Teichner) and a conference in the second week. Both weeks focus on open problems and collaborative work. This structure will greatly benefit early career researchers. Another feature of the meeting that will make it accessible is the theme of the program: promoting interactions between high and low dimensions will mitigate the tendency of technical talks and problems. There are two main research aims for this meeting. The first is to identify settings for synergy from the interaction between high and low dimensions and to make progress on problems in these settings. The second is to produce a high-quality problem list to guide future research in manifold topology. It is our hope that a well-crafted and publicized problem list arising from the collaboration during the meeting will be of long-term benefit to the mathematical community.

An n-manifold is a space which locally resembles n-dimensional Euclidean space. Manifolds of dimension less or equal than 3 are studied using geometric techniques. Manifolds of dimension greater or equal than 5 are studied via surgery theory, which involves a mix of algebraic and differential topology, algebra, and analysis. Dimension 4 is in between; both the high dimensional Whitney Trick and the low-dimensional geometric techniques are only partially successful. The need for our program is that these areas have diverged in the last several decades, to the extent that, often researchers in low/middle/high dimensional topology are not always aware of the current research/techniques in other dimensions. This program will, hopefully, lead to a synergy, benefiting both the experts and the new generation of early career researchers. The website for the event can be found at https://www.matrix-inst.org.au/events/interactions-between-topology-in-high-and-low-dimensions/

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.

Overview

HIL2019 web imageThe purpose of this workshop is to bring focused attention to Hilbert’s 13th problem, and to the broader notion of resolvent degree. While Abel’s 1824 theorem–that the general degree n polynomial is only solvable in radicals for n<4

is well known, less well known is Bring’s 1786 proof that a general quintic is solvable in algebraic functions of only one variable. Hilbert conjectured that for a general sextic, one needs algebraic functions of two variables, and that for a general degree 7 polynomial, one needs algebraic functions of three variables. More generally, it is natural to expect that as n → ∞ , so does the minimal number of variables needed to solve the general degree n polynomial. In a celebrated theorem, Arnol’d and Kolmogorov proved that, at the level of continuous functions, there is no local obstruction to reducing the number of variables to one. Thus, a resolution of Hilbert’s problem must lie deeper. Resolvent degree was introduced by Brauer in order to provide a rigorous statement of these conjectures. While no progress has yet been made on these conjectures, the study of resolvent degree is receiving renewed attention and an influx of ideas from related fields, including:

the theory of essential dimension
uniformization of moduli spaces
braid monodromy
p-adic Hodge theory

This workshop will bring together young and established researchers who work in these fields to explore topics related to Hilbert’s conjectures, to facilitate interaction between subdisciplines, and to lay the groundwork for future progress. The workshop will be organized around mini-courses by experts which will be aimed at 1) conveying the methods that can be brought to bear from each area, and 2) formulating problems concerning resolvent degree that seem particularly tractable using these methods.

Another installment of the Midwest Topology Seminar to be held at the University of Illinois, Urbana-Champaign. More details forthcoming.

Speakers:

• Michael Hopkins
• Jacob Lurie
• Matthew Morrow
• Kirsten Wickelgren

This workshop is dedicated to the promotion of female researchers in the field of homotopy theory and algebraic geometry. The main aim of this workshop is to provide a platform for female researchers (ranging from graduate students to senior experts) to present their work in a friendly environment which stimulates future collaborations. Male participants are very welcome and encouraged to attend. Invited speakers are:

• Natàlia Castellana (Universitat Autònoma de Barcelona)
• Frances Kirwan (University of Oxford)
• Sarah Whitehouse (University of Sheffield)
• Susanna Zimmermann (Université d'Angers)

This workshop is supported by the German Research Foundation through the priority program SPP 1786.

This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.

This is the first of two international conferences representing the full scope of the DFG priority programme "Geometry at Infinity", a research network in differential geometry, geometric topology, and global analysis based at more than 20 German and Swiss universities. Organizers: Christian Bär (Potsdam), Bernhard Hanke (Augsburg), Anna Wienhard (Heidelberg), Burkhard Wilking (Münster).

Dear colleagues,

we are excited to announce a school and workshop

Knots and Braids in Norway (KaBiN)

to be held at NTNU Norwegian University of Science and Technology in Trondheim from May 13 to 17, 2019.

This meeting aims to bring together people with varying points of view who are interested in knots and braids. The school is aimed at Ph.D. students and will cover algebraic aspects and moduli spaces of knots. The workshop will give glimpses into current research directions. We plan for the schedule to allow ample time for discussions and collaboration among participants.

The school consists of two lecture series by:

Ryan Budney (University of Victoria)
Alissa Crans (Loyola Marymount University)

The current list of confirmed workshop speakers is:

Corey Bregman (Brandeis University)
Celeste Damiani (University of Leeds)
Kim Frøyshov (University of Oslo)
Richard Hepworth (University of Aberdeen) 
Victoria Lebed (Université de Caen Normandie)
Arnau Mortier (Dublin City University) 
Mark Powell (Durham University)
Arunima Ray (Max-Planck-Institut für Mathematik Bonn)
Arthur Soulié (Université de Strasbourg)

All interested to come should register via the website, indicating if they would like to contribute and if they need financial support. Priority will be given to graduate students, recent PhDs, and underrepresented minorities. Funds from the project "Pure Mathematics in Norway" of the Bergen Research Foundation with the collaboration of the Tromsø Research Foundation support this event.

The deadline is January 31, 2019. Please apply as early as possible to facilitate our planning process.

https://sites.google.com/view/knots-and-braids-in-norway/home

Best regards,

the organisers

Rachael Boyd (NTNU) Tara Brendle (University of Glasgow) Markus Szymik (NTNU)

Computing various homological invariants of associative algebras (such as Tor and Ext of various modules, Hochschild (co)homology, cyclic homology etc.) has been an active research topic in ring theory for many years. More recently (about 15 years ago), ring theorists became interested in associative algebras up to homotopy, or A-infinity algebras, as a recipe to produce meaningful "higher structures" on classical objects like Yoneda Ext-algebras.

This offers two different perspectives on associative algebras: homological invariants are "Abelian" (i. e. arise when one works with additive categories, e.g. chain complexes of modules over a ring), while homotopical invariants are "non-Abelian" (i. e. arise from non-additive categories, like the category of all differential graded associative algebras). However, these two perspectives are closely related, and it is often possible to recover homological information from the homotopical one, and the other way round. For experts in homotopical algebra on a larger scale (beyond the associative ring theory), this philosophy is already present in works of Stasheff and Hinich on homotopy algebras.

The goal of this workshop is to provide a forum for experts in related areas to share ideas with each other and with younger researchers, identify new promising connections and explore arising research directions.

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.

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

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.

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.