Conference on invertible objects and duality in derived algebraic geometry and homotopy theory

Dates and Location

The conference will take place during the week April 3-7, 2017 at the University of Regensburg in the biology wing, lecture hall H51.

Aims and Scope

The aim of this conference is to present recent advances related to the study of invertible objects, duality, and higher invariants in derived algebraic geometry and homotopy theory. In particular, this conference will include talks on the recent breakthroughs in the study of units, Picard groups, Brauer groups, twists, and module categories.

The activity will consist of a four-part lecture series as well as a number of invited lectures. There will also be an opportunity for junior participants to make short presentations.

Mini-Course

Mike Hopkins Homotopy theory in mathematical modeling / Brauer groups in chromatic homotopy theory (Harvard University)

Invited lectures

Benjamin Antieau Preface to the theory of higher Azumaya algebras (UIC) Video
Paul Balmer Application of tensor-triangular geometry to equivariant stable homotopy theory (UCLA) Video
Agnes Beaudry Gross-Hopkins duals of higher real K-theory spectra (University of Colorado) Video
Denis-Charles Cisinski Generic motivic base change formula (University of Regensburg) Video
David Gepner Elliptic (co)homology and duality (Purdue University) Video
John Greenlees The ubiquity of Gorenstein ring spectra (University of Sheffield) Video
Kathryn Hess Motivic homotopical Galois extensions (EPFL) Video
Mike Hill Mackey functors, Tambara functors, and Andre-Quillen Homology (UCLA) Video
Lennart Meier Towards the Brauer group of TMF (University of Bonn) Video
Sarah Scherotzke A categorification of the Chern character (University of Bonn) Video
Thomas Schick Geometric models for twisted K-homology (University of Göttingen) Video
Urs Schreiber Super topological T-Duality (Institute of Mathematics, Czech Academy of Sciences) Video
Vesna Stojanoska Descent techniques for Picard spectra (University of Illinois) Video
Gabriele Vezzosi Singularity categories and vanishing cycles (University of Florence) Video
Craig Westerland Fox-Neuwirth/Fuks cells, quantum shuffle algebras, and Malles conjecture for function fields (University of Minnesota) Video

Abstracts

Here are the abstracts.

Conference Image

Group photograph

Financial Support

Limited financial support for the conference and younger participants has been provided by the SFB 1085: Higher Invariants, SPP 1786: Homotopy theory and algebraic geometry, and the National Science Foundation.

All applications for financial support received by December 15th, 2016 will be given full consideration.

Registration

Please fill out the registration form.

Statement of Inclusiveness

We (the organizers) affirm that scientific events have to be open to everybody, regardless of race, sex, religion, national origin, sexual orientation, gender identity, disability, age, pregnancy, immigration status, or any other aspect of identity. We believe that such events have to be supportive, inclusive, and safe environments for all participants. We believe that all participants are to be treated with dignity and respect. Discrimination and harassment cannot be tolerated. We are committed to ensuring that this conference follows these principles.

See here for further details.

Practical Information

MAP: Points of Interest.

University Map.

PUBLIC TRANSIT: Local bus system. There are many useful buses typically, but the 6 will suffice for getting to and from the city center and the conference hall (nearest stops are either 'An der Kreuzbreite' or 'Neuprull'). There should be signs pointing to the lecture hall. One can also walk from the 'Universitat' bus stop, which is better served by the bus system. The above maps may prove helpful.

ACCOMMODATION: We will reserve a block of hotel rooms at the Hotel Apollo. Participants will need to book and pay for their own accommodation (promotion code SFB 1085), although the Hotel Apollo should be able to arrange shared rooms for participants with limited financial support (all pre-PhD participants requesting financial support should request a shared room).

Regensburg is a tourist destination and, although April is low season, we encourage guests to book their rooms as early as possible. Here is a list of hotels in the area:

1. Hotel Kaiserhof am Dom (In the city center, must take a bus to the University.)

2. Hotel Muenchner Hof (In the city center, must take a bus to the University.)

3. Hotel Apollo (Near the conference, but limited eating options.)

4. Hotel Jakob (In the center, must take a bus to the University.)

5. Hotel Central (In the city center, must take a bus to the University.)

One can also check the standard alternatives:

1. Hotels.com

2. Airbnb

TRAVEL: One can reach the university by following the instructions here.

INTERNET: Access to eduroam is available throughout the mathematics and biology building. For those without eduroam access we will obtain a temporary guest account through the university.

Organizers

Paul Goerss (Northwestern)
Akhil Mathew (Harvard)
Thomas Nikolaus (Bonn)
Justin Noel (Regensburg)
Vesna Stojanoska (Illinois)

Schedule

Here are the Titles and abstracts.

All lectures will take place in the biology wing, lecture hall H 51

Registration and coffee breaks will be held nearby.

On Monday evening there will be an informal session with pizza and beverages.

	Monday	Tuesday	Wednesday	Thursday	Friday
09:30 - 10:00	Registration and Coffee in front of H51	Coffee
10:00 - 10:50	Greenlees	Hopkins	Hopkins	Hopkins	Hopkins
10:50 - 11:15	Coffee
11:15 - 12:05	Schick	Scherotzke Group photo directly afterwards	Free	Hess	Balmer
12:05 - 14:00	Lunch				END OF SCHOOL
14:00 - 14:50	Stojanoska	Antieau	Free	Beaudry
14:50 - 15:15	Coffee		Free	Coffee
15:15 - 16:05	Cisinski	Gepner	Free	Hill
16:15 - 17:05	Vezzosi	Schreiber	Free	Westerland
17:30 - 22:00	Informal session	Meier (17:15-18:05)	Free	Free

Excursion

On Wednesday afternoon there will be a nature walk/hike to the Monastery Weltenburg, 'the oldest monastery-brewery in the world.' It has been in operation since 1050 and its 'dunkel' beer has won several awards.

We will meet at 12:20 at the university bus terminal to take a bus to Kelheim and then we will walk from there or you can take the boat ride (very nice in a different way). The hike will be roughly 1.75 hours and runs partially along the Danube river and partially through the forest. Half of the walk will be flat and the second half will involve walking up a non-trivial hill. We will then take a ferry across the river to the monastery. Participants can then enjoy the monastery and the surrounding area and/or enjoy the biergarten.

We will return by bus from the Monastery. The bus will stop at the Hotel Apollo and at the Hauptbahnhof.

General Advice:

Sunscreen and insect repellent are recommended.
Shoes appropriate for walking through the woods are recommended.
You will need CASH for any purchases on the ferry or at the monastery/biergarten.

Informal session schedule

The informal session will begin at 17:30 on Monday evening in H51. Here are the abstracts.

1. Tasos Moulinos, On the Topological K-theory of derived Azumaya algebras

2. Helene Sigloch, Homotopy classification of line bundles over rigid analytic varieties

3. James Cameron, The local cohomology modules of group cohomology rings

4. Dimitar Kodjabachev, Gorenstein duality for topological modular forms with level structure

5. 30 Minute break

6. Kevin Carlson, Prederivators as models of homotopy theories

7. Magdalena Kedziorek, Left-induced model structures

8. 20 Minute break

9.. Husney Parvez Sarwar, K-theory of affine toric varieties

8. Peter Nelson, A Small Presentation for Morava E-theory Power Operations

9. Viktoriya Ozornova, Splitting of TMF0(7)

10. Nicolas Ricka, Motivic modular forms

11. Zhen Huan, Quasi-elliptic cohomology

12. Yue Feng, Topological Fukaya category over E-infinity ring spectra

Registered Participants as of March 27th, 2017

Absmeier, Dominik (Bochum)
Antieau, Ben (UIC)
Arkhipov, Sergey (Aarhus)
Arndt, Peter (Düsseldorf)
El asery, Naima (Casablanca)
Baker, Andrew (Glasgow)
Balmer, Paul (UCLA)
Bandklayder, Lauren (Northwestern)
Barthel, Tobias (Copenhagen)
Beaudry, Agnes (Boulder)
Berman, John (Virginia)
Berry, Eric (Montana State University)
Bhattacharya, Prasit (Notre Dame)
Böhme, Benjamin (Copenhagen)
Bonventre, Peter (Virginia)
Bunke, Ulrich (Regensburg)
Cameron, James (University of Washington)
Campbell, Jonathan (Vanderbilt)
Carlson, Kevin (UCLA)
Cepek, Anna (Montana State University)
Charalambous, Georgios (Cambridge)
Cisinski, Denis-Charles (Regensburg)
Clough, Adrian (UT Austin)
Columbus, Tobias (Karlsruher Institut für Technology)
Conde Lago, Jesús (Universidade de Santiago de Compostela)
Dahlhausen, Christian (Regensburg)
Debray, Arun (UT Austin)
Dotto, Emanuele (Bonn)
Ertl, Veronika (Regensburg)
Feng, Yue (Tsinghua)
Fontes, Ernest E. (UT Austin)
Frankland, Martin (Osnabrück)
Friedrich, Roland (Saarland)
Gagna, Andrea (Aix-Marseille Université)
Gepner, David (Purdue)
Gheorghe, Bogdan (Wayne State)
Goerss, Paul (Northwestern)
Greenlees, John (Sheffield)
Hahn, Jeremy (Harvard)
Hausmann, Markus (Copenhagen)
Hayashi, Takuma (Tokyo)
Heard, Drew (Hamburg)
Hebestreit, Fabian (Bonn)
Hedenlund, Alice (Oslo)
Heine, Hadrian (Osnabrück)
Heller, Jeremiah (University of Illinois)
Hellstrøm-Finnsen, Magnus (NTNU Trondheim)
Henn, Hans-Werner (Strasbourg)
Herr, Leo (CU Boulder)
Hess, Kathryn (EPFL)
Hesse, Jan (Hamburg)
Hill, Mike (UCLA)
Hopkins, Mike (Harvard)
Huan, Zhen (UIUC)
Jin, Fangzhou (Regensburg)
Joachim, Michael (Münster)
Kedziorek, Magdalena (EPFL)
El Khamouri, Fatima Zahra (Hassan University II - Casablanca)
Khan, Adeel (Regensburg)
Körschgen, Alex (Bonn)
Kodjabachev, Dimitar (Sheffield)
Kufner, Hanno (Regensburg)
Francois, Kevin (Toulouse)
Van Koughnett, Paul (Northwestern)
Kumar, Pankag (Skolkovo Institute of Science and Technology)
Land, Markus (Regensburg)
Laures, Gerd (Bochum)
Li, Guchuan (Northwestern)
Luckhardt, Daniel (Göttingen)
Lüders, Morten (Regensburg)
Mazel-Gee, Aaron (Ohio State)
Meier, Lennart (Bonn)
Moulinos, Tasos (UIC)
Nassau, Christian (nullhomotopie)
Naumann, Niko (Regensburg)
Nelson, Peter (Haifa)
Nguyen, Manh Toan (Osnabrück)
Nicotra, Stefano (Liverpool)
Nikolaus, Thomas (Bonn)
Noel, Justin (Regensburg)
Otmani, Hind (Casablanca)
Ozornova, Viktoriya (Bonn)
Patchkoria, Irakli (Bonn)
Peterson, Eric (Harvard)
Pham, Viet-Cuong (University of Strasbourg)
Pohl, Gregor (Heidelberg)
Pol, Luca (Sheffield)
Poliakova, Daria (HSE Moscow)
Prasma, Matan (Regensburg)
Quick, Gereon (NTNU Trondheim)
Quigley, J.D. (Notre Dame)
Raptis, George (Regensburg)
Ray, Catherine (Chicago)
Ricka, Nicolas (Wayne State)
Robalo, Marco (Institut Mathematiques Jussieu)
Rok, Gregoric (Ljubljana)
Sanders, Beren (Copenhagen)
Sagave, Steffen (Nijmegen)
Sarwar, Husney Parvez (Tata Institute of Fundamental Research)
Schäppi, Daniel (Regensburg)
Scherotzke, Sarah (Bonn)
Schick, Thomas (Göttingen)
Schreiber, Urs (CAS)
Schulenberg, Nils (Bochum)
Schulz, Julia (Hamburg)
Seeliger, Nora (Haifa)
Shaul, Liran (Bielefeld)
Shi, Xiaolin Danny (Harvard)
Sia, Charmaine (Indiana)
Sigloch, Helene (Regensburg)
Simkova, Maria (Masaryk University Brno)
Sorokin, Oleksiy (Ivan Franko National University)
Stapleton, Nat (Regensburg)
Stelzer, Manfred (Osnabrück)
Stojanoska, Vesna (UIUC)
Strunk, Florian (Regensburg)
Sulyma, Yuri (UT Austin)
Syed, Tariq (LMU Munich)
Verchinine, Vladimir (Montpellier)
Vezzosi, Gabriele (Florence)
Völkel, Konrad (Osnabrück)
Wen, Joshua (UIUC)
Werndli, Kay (Utrecht)
Westerland, Craig (Minnesota)
Williamson, Jordan (Sheffield)
Wilson, Dylan (Northwestern)
Wimmer, Christian (Bonn)
van Woerden, Koen (Regensburg)
Wong, Richard (UT Austin)
Yang, Xuan-Gottfried
Yoshida, Jun (Tokyo)
Yuan, Allen (MIT)
Zibrowius, Marcus (Düsseldorf)

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