Welcome to MathMeetings.net! This is a list for research mathematics conferences, workshops, summer schools, etc.

There are a few other conference lists available, but this list aims to be more complete by allowing anyone at all to add announcements. Rather than use a wiki, announcement information is stored in database format so that useful search functions can be added as the list grows.

This site began as AlgTop-Conf, for meetings in algebraic topology. It is now expanded to serve other mathematics subjects. Use tag filtering to focus on announcements related to your discipline (see right or below).

Know of a meeting not listed here? Add it now!

New Announcement

Updates 2016-01

  • Now filter announcements by subject tags
  • Form for editing announcements is now the same as that for adding new announcements
  • New 'view' page for each announcement, and announcement data in confirmation emails
  • Select boxes improved with select2 (jquery)

Additional update notes are available in the git repository (GitHub).


Upcoming Meetings

RSS

May 2017

Georgia International Topology Conference

at.algebraic-topology gt.geometric-topology
2017-05-22 through 2017-06-02
University of Georgia
Athens, Georgia; USA

Meeting Type: conference

Contact: see conference website

Description

This is the eighth installment of a major conference in geometric topology and related areas that has been held at the University of Georgia every eight years since 1961. The 2017 conference will include dozens of speakers whose ideas have advanced the field over the last several years. Over two weeks, the conference will provide plenty of time for collaboration and for interaction between junior and senior researchers.

We have significant funding available to support the participation of graduate students and early-career mathematicians; those interested, especially from underrepresented groups, should apply at the conference website.

Princeton-Rider Workshop on the Homotopy Theory of Polyhedral Products

ac.commutative-algebra at.algebraic-topology co.combinatorics gt.geometric-topology
2017-05-29 through 2017-06-02
Princeton University and Rider University
Princeton and lawrenceville NJ; USA

Meeting Type: conference

Contact: Tony Bahri

Description

Cartesian products have embedded within them certain natural subsets which are indexed by combinatorial information. The geometric characterization of these subspaces, known now as polyhedral products, has application in toric geometry and topology, combinatorics,geometric group theory, number theory, homotopy theory and arachnid mechanisms. The workshop will focus on the topology and geometry of these and related spaces.

June 2017

Mathematics Research Communities: Homotopy Type Theory

at.algebraic-topology ct.category-theory lo.logic
2017-06-04 through 2017-06-10
Snowbird Resort, Utah; USA

Meeting Type: MRC workshop

Contact: Chris Kapulkin

Description

none

European Talbot 2017: Dualities in Algebra, Geometry, and Topology

ac.commutative-algebra at.algebraic-topology gt.geometric-topology rt.representation-theory
2017-06-11 through 2017-06-17
Lower Saxony; Germany

Meeting Type: workshop

Contact: Bertram Arnold, Tobias Barthel, Magdalena Kedziorek, and Sean Tilson

Description

The third European Talbot workshop will take place in Germany from June 11 to June 17, 2017. The goal is to bring together a group of 30-35 graduate students and post-docs to work on a focused topic under the guidance of two senior mentors.

This years topic is "Dualities in Algebra, Geometry, and Topology" and is mentored by John Greenlees and Mike Hill. More information can be found at the workshops website website.

Meeting of the Catalan, Spanish, Swedish Math Societies, special session in homotopy theory

at.algebraic-topology gt.geometric-topology
2017-06-12 through 2017-06-15
University of Umeå
Umeå; Sweden

Meeting Type: special session

Contact: Tilman Bauer, Natalia Castellana

Description

Meeting of the Catalan, Spanish, Swedish Math Societies (CAT-SP-SW-MATH)

A joint Meeting of the Catalan, Spanish, Swedish Math Societies (CAT-SP-SW-MATH) will be held in Umeå (Sweden) from 12th to 15th June 2017.

The meeting is a symposium devoted to mathematics at large. The conference is thought as a meeting point between the different areas of mathematics and its applications.

The programme will consist of several plenary lectures, covering a wide range of areas of mathematics, and special sessions devoted to a single topic or area of mathematics.

There is going to be a special session in homotopy theory, chaired by Natalia Castellana and Tilman Bauer, with the following speakers:

Alexander Berglund: Rational homotopy theory of automorphisms of manifolds Federico Cantero: Rational homotopy theory of Thom spaces Cristina Costoya: Polyhedral products in Kahn’s Realizability Problem Felix Wierstra: Hopf invariants in rational homotopy theory Kiko Belchí: Persistent homology: from Stasheff to the hospital Antonio Viruel: On the realizability of group actions Albert Ruiz: On the classification of p-local compact groups over a fixed dis- crete p-toral group Magnus Carlson: Higher obstructions to the embedding problem in Galois theory Carlos Sáez:Finite subgroups of diffeomorphisms of 4-manifolds Thomas Kragh: Waldhausens K-theory of spaces and exact Lagrangian submanifolds Ramón Flores: Burnside groups and idempotent transformations of groups

Conference web page

Everybody is welcome to attend, whether Catalan-Spanish-Swedish or not.

Applied Topology in Bedlewo

at.algebraic-topology gt.geometric-topology
2017-06-25 through 2017-07-01
Adam Mickiewicz University
Bedlewo; Poland

Meeting Type: conference

Contact: Zbigniew Błaszczyk

Description

This will be the second edition of a conference that took place in Bedlewo in July 2013.

Similarly as before, our aim is to bring together scientists from all over the world working in various fields of applied topology, including:

  • topological robotics,
  • topological methods in combinatorics,
  • random topology,

as well as topological data analysis, with emphasis on:

  • neurotopology,
  • materials analysis,
  • computational geometry, and
  • multidimensional persistence.

Algebraic Topology and Representation Theory

at.algebraic-topology rt.representation-theory
2017-06-26 through 2017-06-30
Université de Lille 1
Lille; France

Meeting Type: conference

Contact: Ivo Dell'Ambrogio, Antoine Touzé

Description

The goal of this conference is to gather algebraic topologists and representation theorists around common algebraic interests, such as: group (co)homology, Hopf algebras, equivariant theories, support varieties, functorial and higher categorical methods.

To facilitate interactions between people of different backgrounds, the conference will be enriched by two mini-courses, one more oriented towards algebraic topology and the other towards representation theory.

Stable homotopy theory and p-adic Hodge theory

ag.algebraic-geometry at.algebraic-topology kt.k-theory-and-homology nt.number-theory
2017-06-26 through 2017-06-30
University of Copenhagen, Department of Mathematics
Copenhagen; Denmark

Meeting Type: Masterclass

Contact: Ryo Horiuchi, Martin Speirs, Lars Hesselholt

Description

Stable Homotopy theory and arithmetic geometry are two very active areas of research today. Our speakers, Thomas Nikolaus and Matthew Morrow represent two researchers at the forefront of these areas, working in different but overlapping fields. The overall motivation for this masterclass is to study the relations between these two areas of research.

In recent years stable homotopy theory has seen unexpected applications to arithmetic geometry. In particular the work of Matthew Morrow (in collaboration with Bhargav Bhatt and Peter Scholze) on integral p-adic Hodge theory was, in part, motivated by calculations of topological Hochschild homology for certain arithmetically important rings. Very recently Lars Hesselholt has used the cyclotomic structure on topological Hochschild homology to define a topological version of periodic cyclic homology and used it to give cohomological interpretations of zeta functions for schemes over finite fields. This was in part motivated by new perspectives and results on cyclotomic structures afforded by work of Thomas Nikolaus (in collaboration with Peter Scholze).

The goal of this masterclass is to study this recent progress. In particular we will focus on the work by Nikolaus and Scholze on cyclotomic spectra and the work by Bhatt, Morrow and Scholze giving integral relations between p-adic cohomology theories. The masterclass will consist of two lecture series by Matthew Morrow and Thomas Nikolaus as well as several discussion sessions.

July 2017

Persistent Homology Summer School

ac.commutative-algebra ag.algebraic-geometry at.algebraic-topology
2017-07-03 through 2017-07-07
Fac. Sc and CRMEF Rabat
Rabat; Morocco

Meeting Type: Summer School

Contact: My Ismail Mamouni

Description

The Persistent Homology is a recent and immersive research areas. It is a homology theory adapted in an algorithmic context to the topological data analysis. It keeps track of the homology classes that still remain "persistent" when approaching a topological space by a cloud of points. The persistent homology finds applications in all research areas that involve big datas, including medicine, chemistry, music, linguistics, sports, economics, social sciences, ....

        The course is intended to PhD  students who have already started research in Persistent homology, it can also  inspire  students at the end of their master to start their research in this area and finally it can interest senior and junior researchers for a re-conversion in another field of research

      We plan to schedule 16 hours of courses, 6 hours of open discussion, 3 hours of Lab sessions, and 3 hours of research contributed talks.

Young Topologists Meeting

at.algebraic-topology gn.general-topology gt.geometric-topology kt.k-theory-and-homology
2017-07-03 through 2017-07-07
Stockholm University and KTH
Stockholm; Sweden

Meeting Type: conference

Contact: Ben Ward

Description

The 2017 Young Topologists Meeting will take place in Stockholm from the 3rd to the 7th of July, hosted by KTH and Stockholm University. The conference will be an opportunity for graduate students, recent PhDs and other junior researchers to meet and present their work to each other. In addition to the talks given by the participants, there will be two mini-courses given by Benson Farb (University of Chicago) and Brooke Shipley (University of Illinois at Chicago).

For further information see: www.math-stockholm.se/konferenser-och-akti/young-topologists-meeting-2017-1.670396

Registration will open the 27th of January. We will be able to cover accomodation for approximately 100 participants. In addition, we are applying for NSF funding to cover travel expenses for participants from US institutions.

The Young Topologists Meeting 2017 is made possible by the generous support of:

  • The Foundation Compositio Mathematica
  • Stockholm Mathematics Centre

Floer homology and homotopy theory: summer school and conference

at.algebraic-topology gt.geometric-topology sg.symplectic-geometry
2017-07-10 through 2017-07-21
UCLA
Los Angeles, CA; USA

Meeting Type: Summer school

Contact: Andrew Blumberg

Description

These two events will bring together symplectic geometers, low dimensional topologists, and algebraic topologists. The main goal will be to explore the use of homotopy theoretic methods in Floer theory. The summer school (July 10-15) will cover background material, aimed at familiarizing students and researchers with the material in each of the three fields. It will be followed by a research conference (July 17-21).

Workshop on Infinity-Operads and Applications

at.algebraic-topology ct.category-theory
2017-07-12 through 2017-07-14
Universität Osnabrück
Osnabrück; Germany

Meeting Type: workshop

Contact: Hongyi Chu, Joana Cirici, Oriol Raventós, Markus Spitzweck

Description

Infinity-operads have attracted a great deal of attention from the homotopy theory community and their potential for applications is now being explored in different fields. This workshop will give its participants the chance to learn about the existing models for infinity operads, the relation between them and some of their most recent applications. The workshop will consist of three mini-courses as well as contributed talks. The participants will be assumed to be familiar with the basic theory of ordinary operads and homotopy theory (that is basic model category theory and basic infinity-category theory).

Homotopy Theory: tools and applications

at.algebraic-topology
2017-07-17 through 2017-07-21
University of Illinois at Urbana-Champaign
Urbana-Champaign, Illinois; USA

Meeting Type: conference

Contact: Daniel Davis, Mark W. Johnson, Charles Rezk, Vesna Stojanoska

Description

Preliminary Announcement.

The aim of the conference is to survey recent advances in the fundamental tools of homotopy theory (including abstract homotopy theory, equivariant homotopy, obstruction-theoretic methods), to highlight future directions of research, including applications to chromatic homotopy theory, motivic homotopy theory, and derived algebraic geometry.

Speakers:
Agnes Beaudry, University of Chicago
Mark Behrens, University of Notre Dame
David Blanc, University of Haifa
Anna Marie Bohmann, Vanderbilt University
Hans-Werner Henn, University of Strasbourg
Kathryn Hess, EPFL
Mike Hopkins, Harvard University
Marc Hoyois *, MIT
Rick Jardine, University of Western Ontario
Magdalena Kedziorek, EPFL
Nitu Kitchloo, Johns Hopkins University
Tyler Lawson, University of Minnesota
Jacob Lurie, Harvard University
Haynes Miller, MIT
Jack Morava, Johns Hopkins University
Doug Ravenel, University of Rochester
Birgit Richter, University of Hamburg
Brooke Shipley, University of Illinois at Chicago
Zhouli Xu, University of Chicago
Inna Zakharevich, University of Chicago

*to be confirmed

Others interested in speaking are encouraged to contact the organizers.

Further information will become available at the conference website
http://www.math.illinois.edu/homotopy2017/index.html
and
questions to the conference organizers are welcome at
homotopy2017@math.uiuc.edu

Organizers:

Daniel Davis, University of Louisiana at Lafayette
Mark W. Johnson, Penn State Altoona
Charles Rezk, University of Illinois at Urbana-Champaign
Vesna Stojanoska, University of Illinois at Urbana-Champaign

Topological and Geometric Methods in Quantum Field Theory (NSF-CBMS)

at.algebraic-topology dg.differential-geometry gt.geometric-topology mp.mathematical-physics
2017-07-31 through 2017-08-04
Montana State University
Bozeman, Montana; USA

Meeting Type: Workshop, summer school,

Contact: David Ayala, Ryan Grady

Description

NSF-CBMS conference: "Topological and Geometric Methods in Quantum Field Theory." http://www.math.montana.edu/cbms/ 31 July - 4 August 2017, Bozeman, Montana.

Expert Participants. Dan Freed (principle lecturer) Agnes Beaudry Robert Bryant Sam Gunningham Max Metlitski David Morrison Andy Neitzke

Abstract. This event will be framed around a series of 10 somewhat self-contained lectures by Dan Freed concerning recent work using stable homotopy theory for predictive results in topological phases of matter. Other key experts will facilitate supplemental discussion sessions with the intent of offering background, context, and examples. The expertise of these participants will represent differential geometry, quantum field theory, and algebraic topology.
This event will be especially designed for graduate students and recent graduates, as well as experienced researchers aiming to enhance their pool of workable knowledge.

Registration. Please register through the event webpage: http://www.math.montana.edu/cbms/ . Deadline for registration is 19 March 2017; there is no registration fee.

There are NSF funds to fully support 30 participants, notably graduate students and recent graduates; these funds will cover food, board, and travel (within the United States). Application for such funding is part of the registration process.

Location. Bozeman, Montana, is an especially splendid place to be through this period of the summer. There are a host of trails near to town, and there is a modest, though active, downtown district.

For any further inquiries please send an email to Ryan Grady: ryan.grady1 at montana.edu .

August 2017

Summer School on Trace Methods in Algebraic K-Theory

at.algebraic-topology kt.k-theory-and-homology nt.number-theory
2017-08-07 through 2017-08-11
Indiana University
Bloomington, Indiana; USA

Meeting Type: summer school

Contact: Benjamin Antieau

Description

none

Topology Ecuador 2017

at.algebraic-topology kt.k-theory-and-homology oa.operator-algebras
2017-08-14 through 2017-08-18
Universidad San Francisco de Quito, Galapagos Science Center
Puerto Baquerizo Moreno, Galápagos; Ecuador

Meeting Type: conference

Contact: Daniela Egas, Andrea Moreira, John Skukalek, Marc Stephan

Description

This conference will cover a wide range of topics from algebraic topology to non-commutative geometry. Its purpose is to contribute to the development of these fields in Ecuador and to provide a meeting point for Latin-American mathematicians with other experts from around the world.

Homotopy Theory in the Ecliptic: Chromatic, Equivariant, and Motivic Mathematics

at.algebraic-topology gt.geometric-topology
2017-08-18 through 2017-08-21
Reed College
Portland, Oregon; USA

Meeting Type: conference

Contact: Agnes Beaudry, Irina Bobkova, Safia Chettih, Mike Hill, John Lind, Kyle Ormsby, Angelica Osorno

Description

none

Low-dimensional Topology and Number Theory

gt.geometric-topology nt.number-theory
2017-08-20 through 2017-08-26
Mathematisches Forschungsinstitut Oberwolfach
Oberwolfach; Germany

Meeting Type: invitational conference

Contact: see conference website

Description

Organisers

Paul E. Gunnells, Amherst

Walter D. Neumann, New York

Adam S. Sikora, New York

Don B. Zagier, Bonn

September 2017

Locally Symmetric Spaces: Analytical and Topological Aspects

ag.algebraic-geometry gt.geometric-topology nt.number-theory rt.representation-theory
2017-09-01 through 2018-04-30
Institute for Advanced Study
Princeton, NJ; USA

Meeting Type: long-term research program

Contact: see conference website

Description

During the 2017-18 academic year, the School will have a special program on Locally Symmetric Spaces: Analytical and Topological Aspects. Akshay Venkatesh of Stanford University will be the Distinguished Visiting Professor.

The topology of locally symmetric spaces interacts richly with number theory via the theory of automorphic forms (Langlands program). Many new phenomena seem to appear in the non-Hermitian case (e.g., torsion cohomology classes, relations with mixed motives and algebraic K-theory, derived nature of deformation rings). One focus of the program will be to try to better understand some of these phenomena.

Much of our understanding of this topology comes through analysis ("Hodge theory"). Indeed harmonic analysis on locally symmetric spaces plays a foundational role in the theory of automorphic forms and is of increasing importance in analytic number theory. A great success of such harmonic analysis is the Arthur-Selberg trace formula; on the other hand, the analytic aspects of the trace formula are not fully developed, and variants such as the relative trace formula are not as well understood. Thus analysis on such spaces, interpreted broadly, will be another focus of the program.

Workshop: Non-Positively Curved Groups and Spaces

dg.differential-geometry gt.geometric-topology mg.metric-geometry
2017-09-18 through 2017-09-22
University of Regensburg
Regensburg; Germany

Meeting Type: workshop

Contact: Alexander Engel

Description

There will be 3 mini-courses (each 3 lectures 75 min. long) and around 9 invited and contributed talks. Deadline for applications for contributed talks is May 15th, 2017.

October 2017

Workshop on motivic and equivariant homotopy theory

ag.algebraic-geometry at.algebraic-topology
2017-10-04 through 2017-10-07
Universität Osnabrück
Osnabrück; Germany

Meeting Type: workshop

Contact: Martin Frankland, Manh Toan Nguyen, Konrad Voelkel

Description

See the website.

November 2017

Special Session in Homotopy Theory

at.algebraic-topology ct.category-theory
2017-11-04 through 2017-11-05
University of California - Riverside
Riverside, CA; USA

Meeting Type: Special Session

Contact: Jonathan Beardsley

Description

Special session in homotopy theory at the AMS Western Sectional Meeting.

Winter school: Categorification, representation theory and symplectic geometry

gt.geometric-topology qa.quantum-algebra rt.representation-theory sg.symplectic-geometry
2017-11-20 through 2017-11-24
University of Bonn
Bonn; Germany

Meeting Type: Winter school

Contact: Anne-Laure Thiel, Daniel Tubbenhauer

Description

There is a fruitful interplay between categorification, representation theory and symplectic geometry, and our intention is to highlight some of them in detail.

We hope to bring together researchers as well as students who want to learn more about the various presented aspects of the broad fields categorification, representation theory and symplectic geometry.

Please make sure that you register due to seats constraints. (Application deadline is the 31th of July 2017.)

Workshop: Categorification, representation theory and symplectic geometry

gt.geometric-topology qa.quantum-algebra rt.representation-theory sg.symplectic-geometry
2017-11-27 through 2017-12-01
University of Bonn
Bonn; Germany

Meeting Type: Workshop

Contact: Anne-Laure Thiel, Daniel Tubbenhauer

Description

There is a fruitful interplay between categorification, representation theory and symplectic geometry, and our intention is to highlight some of them in detail.

We hope to bring together researchers as well as students who want to learn more about the various presented aspects of the broad fields categorification, representation theory and symplectic geometry.

Please make sure that you register due to seats constraints. (Application deadline is the 31th of July 2017.)

July 2018

Higher structures in homotopy theory

at.algebraic-topology gt.geometric-topology
2018-07-02 through 2018-07-06
Isaac Newton Institute for Mathematical Sciences
Cambridge, England; UK

Meeting Type: conference

Contact: Clark Barwick, Julie Bergner, Ieke Moerdijk, Stefan Schwede, Paul Goerss

Description

Part of the Semester Programme "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 particular workshop will focus on the last of these themes.

August 2018

International Congress of Mathematicians

ac.commutative-algebra ag.algebraic-geometry ap.analysis-of-pdes at.algebraic-topology ca.classical-analysis-and-odes co.combinatorics ct.category-theory cv.complex-variables dg.differential-geometry ds.dynamical-systems fa.functional-analysis gm.general-mathematics gn.general-topology gr.group-theory gt.geometric-topology ho.history-and-overview it.information-theory kt.k-theory-and-homology lo.logic mg.metric-geometry mp.mathematical-physics na.numerical-analysis nt.number-theory oa.operator-algebras oc.optimization-and-control pr.probability qa.quantum-algebra ra.rings-and-algebras rt.representation-theory sg.symplectic-geometry sp.spectral-theory st.statistics-theory
2018-08-01 through 2018-08-09
Rio de Janeiro; Brazil

Meeting Type: international congress

Contact: see conference website

Description

Satellite conferences will appear later with their own entries.

Equivariant and motivic homotopy theory

at.algebraic-topology gt.geometric-topology
2018-08-13 through 2018-08-17
Isaac Newton Institute for Mathematical Sciences
Cambrige, England; UK

Meeting Type: workshop

Contact: John Greenlees, Lars Hesselholt, Mike Hill, Dan Isaksen, Paul Goerss

Description

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 equivariant homotopy theory and its applications.

September 2018

Derived algebraic geometry and chromatic homotopy theory

at.algebraic-topology gt.geometric-topology
2018-09-24 through 2018-09-28
Isaac Newton Institute for Mathematical Sciences
Cambridge, England; UK

Meeting Type: conference

Contact: Mark Behrens, David Gepner, Paul Goerss, Mike Hopkins, Tyler Lawson,

Description

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 derived algebraic geometry and the interplay with stable homotopy theory.

December 2018

Manifolds

at.algebraic-topology gt.geometric-topology
2018-12-03 through 2018-12-07
Isaac Newton Institute for Mathematical Sciences
Cambrige, England; UK

Meeting Type: workshop

Contact: David Ayala, Oscar Randal-Williams, Ulrike Tillmann, Michael Weiss, Paul Goerss

Description

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.

January 2019

Derived Algebraic Geometry

ag.algebraic-geometry at.algebraic-topology nt.number-theory
2019-01-22 through 2019-05-24
MSRI
Berkeley, CA; USA

Meeting Type: research program

Contact: see conference website

Description

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.

March 2019

Derived algebraic geometry and its applications

ag.algebraic-geometry at.algebraic-topology mp.mathematical-physics nt.number-theory rt.representation-theory
2019-03-25 through 2019-03-29
MSRI (Mathematical Sciences Research Institute)
Berkeley, CA; USA

Meeting Type: conference

Contact: see conference website

Description

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.