Teleconference on categorified knot invariants
Higher Geometric Structures along the Lower Rhine XI, March 89, 2018
This is the eleventh of a series of short workshops jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, and Utrecht, all situated along the Lower Rhine. The focus lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics.
Webpages of the previous meetings: I (MPIM Bonn), II (Nijmegen), III (Utrecht), IV (Bonn), V (Nijmegen), VI (Utrecht), VII (Leuven), VIII (Bonn), IX (Nijmegen), X (Utrecht)
Speakers
Davide Alboresi
Yaël Fregier
Owen Gwilliam
Cary Malkievich
Lennart Meier
Joost Nuiten
Steffen Sagave
Program
Here are the links to the program and the abstracts as soon as they become available.
Registration
To register please use the registration webform. There is no registration fee. For any further inquiries please send an email to LowerRhineXI@mpimbonn.mpg.de.
Financial support
Limited financial support is available. If you need support, please add a request on your registration webform with a brief justification. Please note that the workshop is relatively local in scope, so that we might be able to cover your accommodation but probably not your travel expenses. The Deadline is February 18, 2018.
Conference dinner
The conference dinner will be on Thursday evening at 18:00h at the institute.
Practical information
For practical information such as how to get to the institute and a list of hotels see here.
Last changed on January 22, 2018 by Christian Blohmann
3rd JapaneseGerman Number Theory Workshop, November 20  24, 2017
3rd JapaneseGerman Number Theory Workshop
November 20  24, 2017
Here you can find the official homepage
Organizers
 German Organizers : Jonas Kaszian (University of Cologne), Pieter Moree (MPIM)
 Japanese Organaizers : Hiroki Aoki (Tokyo University of Science), Koji Tasaka (MPIM/Aichi Prefectural University)
Speakers
Sho Takemori (MPIM)
Tomomi Ozawa (Univ. Paris 13)
Kenji Makiyama (Kyoto Sangyo Univ.)
Renhe Su (Kyoto Univ.)
Nobuo Sato (Kyoto Univ.)
Hiraku Atobe (Tokyo Univ.)
Shingo Sugiyama (Kyushu Univ.)
Minoru Hirose (Kyushu Univ.)
Toshiki Matsusaka (Kyushu Univ.)
Shun'ichi Yokoyama (Kyushu Univ.)
Hiroshi Sakata (Waseda Univ Senior High School)
Hidetaka Kitayama (Wakayama Univ.)
Hiroaki Narita (Kumamoto Univ.)
Takashi Nakamura (Tokyo Univ. of Science)
Hiroki Aoki (Tokyo Univ. of Science)
Claudia AlfesNeumann (University of Cologne)
Jan Bruinier (TU Darmstadt)
Steffen Löbrich (University of Cologne)
Markus Schwagenscheidt (TU Darmstadt)
Annalena Wernz (RWTH Aachen)
Registration
To register please use the registration webform. There is no registration fee. For any further inquiries please send an email to JPNGER2017@mpimbonn.mpg.de.
Contributed Talk
If you would like to give a contibruted talk, please register until October 15, 2017.
Hotel reservations
If you would like us to make a hotel reservation for you, please state this on the registration webform. We can only honor requests for hotel reservations made by October 31, 2017. If you would like to make a hotel reservation by yourself you will find a list of hotels here.
Workshop "Young Researchers in String Mathematics", November 27  30, 2017
Workshop "Young Researchers in String Mathematics"
November 27  30, 2017
The workshop is an occasion to foster interactions and initiate new collaborations between young researchers active in Germany and nearby countries, who are all interested in mathematical aspects of string theory: mirror symmetry, enumerative geometry of curves (GromovWitten theory, DonaldsonThomas, stable pair invariants, ...) and their modularity, integrability, and algebraic properties, tropical geometry, topological recursion, wallcrossing phenomena and Bridgeland stability conditions, relations to gauge theory, geometric quantization, conformal field theory, etc.
Organizers
Murad Alim (Universität Hamburg) and Gaëtan Borot (MPIM)
Speakers
Andrea Brini (CNRS Montpellier/Imperial College)
Miranda Cheng (University of Amsterdam)
Michele Cirafici (IST Lisboa)
Sara Angela Filippini (Cambridge University)
Michel van Garrel (Universität Hamburg)
Owen Gwilliam (MPIM)
Lotte Hollands (HeriotWatt University, Edimburgh)
Victoria Hoskins (Freie Universität Berlin)
Hans Jockers (BCTP Bonn)
Christian Lehn (Universität Chemnitz)
Jan Manschot (Trinity College Dublin)
Elli Pomoni (DESY Hamburg)
Johannes Rau (Universität Tübingen)
Thomas Reichelt (Universität Heidelberg)
Helge Ruddat (Universität Mainz)
Sarah Scherotzke (Universität Münster)
Maxim Smirnov (Universität Augsburg/MPIM)
Piotr Sułkowski (University of Warsaw)
Di Yang (MPIM)
Jie Zhou (Universität Köln)
Confirmed participants
Aghaei, Nezhla (University of Bern) 
Ai, Xiaohua (MPIM Bonn) 
Banerjee, Sibasish (MPIM Bonn) 
Beck, Florian (University of Hamburg) 
Belliard, Raphaël (DESY) 
Caputo, Raffaele (University of Hamburg) 
Ciosmak, Paweł (Univeristy of Warsaw) 
ComanLohi, Ioana (DESY) 
El Hilany, Boulos (Eberhard Karls Universität Tübingen) 
Felten, Simon (JGU Mainz) 
Figiel, Troy (DESY) 
Fierro Cota, Cesar (Physikalisches Institut der Universität Bonn) 
Fischbach, Fabian (BCTP Bonn) 
Foster, Tyler (MPIM Bonn) 
Gabele, Tim (Hamburg Universität) 
GarciaFailde, Elba (MPIM Bonn) 
Gerhardus, Andreas (BCTP Bonn) 
Giacchetto, Alessandro (MPIM Bonn) 
Huerta, John (IST Lisboa) 
Iakovidis, Nikolaos (Uppsala University) 
Kazhymurat, Aknazar (NIS Almaty on Physics and Mathematics) 
Kontrec, Ana (University of Zagreb) 
Kramer, Reinier (Universiteit van Amsterdam) 
Larraguivel, Helder (University of Warsaw) 
Lewanski, Danilo (MPIM Bonn) 
Ludewig, Matthias (MPIM Bonn) 
Manabe, Masahide (MPIM Bonn) 
Maunder, James (MPIM Bonn) 
Mertens, Michael H. (University of Cologne) 
Mukhopadhyay, Swarnava (MPIM Bonn) 
Nazaroglu, Caner (Universität zu Köln) 
Nega, Christoph (BCTP Bonn) 
Ninad, Urmi (University of Bonn) 
Noshchenko, Dmitry (IKIR FEB RAS) 
Rabinovich, Eugene (MPIM Bonn) 
Rahmati, Mohammad Reza (UNAM) 
Ren, Jie (MPIM Bonn) 
Rüter, Philipp (HeriotWatt University) 
Safari, Reza (BCTP Bonn) 
Saha, Arpan (University of Hamburg) 
Schimannek, Thorsten (BCTP, University of Bonn) 
Su, Changjian (IHES) 
Sutherland, Tom (Johannes Gutenberg Universität Mainz) 
Tavakol, Mehdi (MPIM Bonn) 
Tonita, Valentin (MPIM Bonn) 
Vasko, Petr (University of Warsaw) 
Vogrin, Martin (University of Hamburg) 
Yagi, Junya (Perimeter Institute) 
Zenkevich, Yegor (Universita degli studi di Milano Bicocca) 
Registration
The registration is closed.
For any further inquiries please send an email to YRMS2017@mpimbonn.mpg.de.
Poster session
A poster session will take place Tuesday afternoon. PhD students and postdocs are welcome to submit their poster proposal (title and abstract) by October 31, 2017. The recommended size for posters is A0 or A1.
Financial support
Limited financial support is available. If you need support, you can add your request on the registration webform with a brief justification. Requests for financial support will have to be made by September 30, 2017.
Hotel reservations
If you would like us to make a hotel reservation for you, please state this on the registration webform. We can only honor requests for hotel reservations made by October 31, 2017. If you would like to make a hotel reservation by yourself you will find a list of hotels here.
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Summer School "Modular forms are everywhere"
Summer School on "Modular Forms are everywhere", May 1519, 2017
Organizers
Speakers
 Martin Möller (Universität Frankfurt)
 Fernando Rodriguez Villegas (ICTP)
 Don Zagier (MPIM)
Location
Max Planck Institute for Mathematics
How to get here
Young Women in Geometry
Registration Participants Practical Information
This meeting is part of the series of workshops Young Women in...
The main lectures will be given by (note that the list of our main speakers is updated)
The workshop provides a platform for female graduate students and postdocs in Geometry to present their research. The main lectures will be complemented by participants' talks and a poster exhibition.
Everybody is welcome to attend the workshop. We encourage all participants  male and female  to contribute a poster to our poster sessions and to apply for a contributed talk.
Title and abstract of your talk should be submitted to YWGeometry@mpimbonn.mpg.de by February 15, 2017.
Limited financial support is available for female participants. Requests for funding can be made during registration. For full consideration, submit your funding request by January 15, 2017.
We gratefully acknowledge the financial support from the Hausdorff Center for Mathematics and the Max Planck Institute for Mathematics.
Click on image for a larger version of the group picture:
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Higher Geometric Structures along the Lower Rhine VIII
This is the eighth of a series of short workshops jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, Utrecht and Leuven, all situated along the Lower Rhine. The focus lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics.
Webpages of the previous meetings: I (MPIM Bonn), II (Nijmegen), III (Utrecht), IV (Bonn), V (Nijmegen), VI (Utrecht), VII (Leuven)
Speakers
Stefan Behrens
Emanuele Dotto
Brice le Grignou
Ioan Marcut
Joost Nuiten
Pavel Safronov
Bernardo Uribe
Program
Here are the links to the program and the abstracts as soon as they become available.
Registration
To register please use the registration webform. There is no registration fee. For any further inquiries please send an email to LowerRhineVIII@mpimbonn.mpg.de.
Financial support
Limited financial support is available. If you need support, please add a request on your registration webform with a brief justification. Please note that the workshop is relatively local in scope, so that we might be able to cover your accommodation but probably not your travel expenses. The Deadline is November 14, 2016.
Conference dinner
The conference dinner will be on Thursday evening at 18:00h at the University Club.
Practical information
For practical information such as how to get to the institute and a list of hotels see here.
Last changed on September 1, 2016 by Christian Blohmann
Workshop on Homotopy Type Theory
The workshop will give the participants the chance to discuss of current problems in areas of active research in homotopy type theory. Each day will start with a lecture series by Vladimir Voevodsky on "Dependent Type Theory", followed by open seminars in which workshop participants can give short presentations on their research.
The lecture series by Vladimir Voevodsky was recorded and can be found here .
Workshop coordinator:
Richard Garner (Macquarie University)
Preliminary list of participants
Schedule
Wednesday  Thursday  Friday  Saturday  Sunday 

10:0011:00  10:0011:00  10:0011:00  10:0011:00  10:0011:00 
Lunch break  Lunch break  Lunch break  Lunch break  Lunch break 
14:3016:00 Chris Kapulkin  13:3015:00 Benno van den Berg  13:3015:00 Bas Spitters  14:3016:00 Egbert Rijke  13:3014:15 Dan Grayson 

 14:1515:00 Simon Hubert  
15:0016:00 Clemens Berger  15:0015:30 Tea  15:0015:30 Tea  
16:0016:30 Tea  16:0016:30 Tea  15:3017:00 Ulrik Buchholtz  16:0016:30 Tea  15:3016:15 Bas Spitters 
16:3018:00 Eric Finster  16:3018:00 Peter Lumsdaine  16:3018:00 Thomas Streicher  16:1517:00 Andrej Bauer  
17:0017:45 Peter Lumsdaine 
Lectures by Vladimir Voevodsky: "Dependent Type Theories"
Abstract: Modern dependent type theories exist mostly in the form of computer programs. As such they are objects of the physical reality more than they are objects of the mathematical one. For three decades the world of type theories was relatively calm  innovation was largely occurring in the layers of programming above the type theories leading to proof assistants with more and more sophisticated systems for notation, implicit arguments and tactics.
The discovery of the univalent models led to the addition of new features to the existing type theories as well as to the development of entirely new ones such as cubicaltt. Eventually, these new type theories will become the cores of proof assistants with much more convenient than before environments for formal verification of mathematical arguments.
It is clear that the only way to ensure that these new proof assistants are reliable  that any proof of “false” in such a proof assistant can be mechanically transformed into a proof of “false” in one of the “consistency standards”, is to have a system where a new proof assistant has to be formally certified using an already certified proof assistant against an already certified formal system before it can become accepted as a reliable tool in pure mathematics.
The strongest consistency standard available in pure mathematics is ZFC. This means that as a prerequisite for such a certification system we need to have a mathematical theory of dependent type theories that can be formalized in ZFC. At the moment only fragments of this future theory exist. I will give an introduction to my vision of the theory by describing these fragments and pointing out the gaps.
Organizing committee
Registration
To register please use this registration webform. There is no registration fee. For any further inquiries please send an email to htt2016@mpimbonn.mpg.de.
Hotel reservations
If you would like us to make a hotel reservation for you, please state this on the registration webform. We can only honor requests for hotel reservations made by January 31, 2016. If you would like to make a hotel reservation by yourself you will find a list of hotels here.
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Seminar AachenBonnKölnLilleSiegen on Automorphic Forms
This is the 47th meeting of the joint FrenchGerman seminar on automorphic forms
which is organized by the universities of the five cited cities. Everybody who is interested in
automorphic forms is welcome. We encourage in particular young researchers to participate
and to report on their work in one of our meetings. For further information concerning this
meeting please send an email to moree$@$mpim$$bonn$.$mpg$.$de
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BICMRHCM: Beijing meets Bonn
The purpose of this workshop is to enhance scientific exchange with the German math community and also advertise the postdoc program at BICMR (Beijing International Center for Mathematical Research).
Chinese participants.
 Gang Tian (Differential Geometry）
 Xiaobo Liu (Symplectic geometry and Mathematical Physics)
 Chenyang Xu (Algebraic Geometry)
 Ruochuan Liu (Number theory)
 Bohan Fang (Mathematical Physics)
 Renjie Feng (Complex Geometry)
Mathematicians working in Bonn and speaking:
 Werner Ballmann (Differential Geometry, acting director starting Nov. 2)
 Geordie Williamson (Representation theory)
 Tobias Dyckerhoff (Noncommutative algebraic geometry, mathematical physics)
 Wolfgang Lück (algebraic topology)
 KarlTheodor Sturm (stochastic analysis)
 Michael Meier (chief administrator HCM)
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Workshop on Homotopy theory, manifolds, and field theories
This workshop is part of our Trimester Program at the Hausdorff Institute (HIM)
We are inviting selected speakers to expose their current work, related to the themes of the program. In addition to the HIM members and the Bonn topology community, our limited capacity only allows for about 20 outside participants and we now solicit applications. By registering below, you can apply for participation/funding.
In order to help planning this event, we ask every participant to register, even if you are at Uni Bonn, HIM or MPIM.
Haynes Miller : "Localization in Homotopy Theory" lecture notes and video are now available. ^{NEW}
Confirmed Speakers
Registration
To register please use the registration webform. There is no registration fee.
Financial support
Limited financial support is available. If you need support, please add a request on your registration webform with a brief justification. Please note that the workshop is relatively local in scope, so that we might be able to cover your accommodation but probably not your travel expenses.
Practical information
For practical information such as how to get to the institute and a list of hotels see here.
Workshop: Geometric quantization and topological recursion
Goal: The workshop aims at establishing bridges between the geometric quantization of moduli spaces, and the theory of the topological recursion, continuing earlier discussions initiated by some of the participants. As an application, we have in view the understanding of the allorder asymptotics of quantum knot invariants, like the knot state ensuing from the WittenReshetikhinTuraev construction, or the colored Jones polynomial.
At this occasion, two 5h minicourses will be held, 9h11h every day of the week:
Recordings of the minicourses are available here
The Hitchin connection and the WittenReshetikhinTuraev TQFT
Jørgen Ellegaard Andersen (QGM Aarhus)
We will review the relevant moduli spaces of flat connections which forms the corner stone in the construction of quantum ChernSimons theory from a gauge theory point of view. We will further review the construction of the Hitchin connection in the bundles over Teichmüller space, which are obtained by applying geometric quantization to these moduli spaces. Following this, we will discuss the asymptotics of the Hitchin connection near certain points on the Thurston boundary of Teichmüller space. This will allow us to define both, the unitary structure preserved by the Hitchin connection, the handlebody boundary state vector and curve operators. We will then discuss their relations to Toeplitz operators and obtain asymptotics results about these TQFT. If time allows, we will also discuss quantum ChernSimons theory with complex gauge group.
Topological recursion and moduli spaces
Bertrand Eynard (IPHT CEA Saclay & CRM Montréal)
The lecture will start with an introduction to the topological recursion. Then, we shall explain the proof of the theorem relating topological recursion to integrals over moduli spaces of curves. The last part will focus on the notion of quantum curves. Some explicit examples will be treated, in particular the finite reductions of KdV.
Extra talk on Wednesday 26, 4.30pm:
Topological recursion for ChernSimons theory
Gaetan Borot
We will review what is known on the application of topological recursion to ChernSimons theory, and informally summarize the relations we expect between geometric quantization of character varieties and topological recursion.
Extra talk on Friday 28, 1.00pm (Seminar room, next to Lecture Hall):
Hitchin system and quantum curves
Motohico Mulase
Two regular MPIM seminars will be related to the topic of the workshop:
Topology seminar, Monday 4.30pm
Graphical obstructions to the surjectivity of the higher order Johnson homomorphism
Jim Conant
Oberseminar, Thursday 3.00pm
Givental quantization procedure and computation of GromovWitten invariants by topological recursion
Nicolas Orantin
The remaining time will be devoted to discussions among the participants.
Participants: Raphaël Belliard, Leonid Chekhov, James Conant, Olivia Dumitrescu, Gregor Masbaum, Pavel Mnev, Motohico Mulase, Werner Nahm, Nicolas Orantin, François Petit, Nuño Romao, Emanuel Scheidegger, Shehryar Sikander, Tom Sutherland, Szilard Szabo, Roland van der Veen.
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Motivic structures on quantum cohomology and pencils of CalabiYau motives. Final reports
The goal is to report on the progress made since the first meeting in 2010 on a variety of subjects, including:
 The arithmetic of mirror families and quantum motives.
 Automorphicity of the classical CalabiYau motives.
 Mirror objects in characteristic p and respective automorphic representations.
 Extremal Laurent polynomials and their analogieswith modular families over rational base.
 Congruence properties of Galois representations in mirror families andrelation to Fano topologies.
 Motivic fibrations over G_m and generalizations of GrossKoblitz.
 The crystalline approach to Galois representations of the field of rational functions in finite characteristic.
 Frobenius manifolds, almost Frobenius manifolds and Fmanifolds Isomonodromic deformations.
 Monodromies of (almost) Frobenius manifolds.
 The geometricity conjecture.
 Dubrovin's conjecture
 gamma conjecture I, gamma conjecture II.
 Linearizing GromovWitten calculus.
 Tannakian formalism and
 GromovWitten.
 Quantum motives.
 Affine Grassmannians and quantum corrections to geometric Satake.
Speakers/participants:
 T. Coates
 A. Corti
 B. Dubrovin
 N. Dummigan
 V. Gritsenko
 H. Iritani
 A. Kasprzyk
 A. Kresch
 E. Mann
 A. Mellit
 F. RodriguezVillegas
 J. Stienstra
 A. Strangeway
 P. Vanhove
 D. van Straten
 M. Watkins
 R. Weissauer
 D. Zagier
Higher Geometric Structures along the Lower Rhine IV
This is the fourth of a series of short workshops jointly organized by the Geometry/Topology groups in Bonn, Nijmegen, and Utrecht, all situated along the Lower Rhine. The focus lies on the development and application of new structures in geometry and topology such as Lie groupoids, differentiable stacks, Lie algebroids, generalized complex geometry, topological quantum field theories, higher categories, homotopy algebraic structures, higher operads, derived categories, and related topics.
Webpages of the previous meetings: I (MPIM Bonn), II (Nijmegen), III (Utrecht)
Speakers
Dimitri Ara (Nijmegen)
Michael Batanin (Macquarie University, Sydney/MPIM)
Pedro Frejlich (Utrecht)
Bas Janssens (Utrecht)
Martin Markl (Prague/MPIM)
Eckhard Meinrenken (University of Toronto)
Matan Prasma (Nijmegen)
Program
Her are the links to the program and the abstracts as soon as they become available.
Registration
To register please use the registration webform. There is no registration fee. For any further inquiries please send an email to LowerRhine@mpimbonn.mpg.de.
Financial support
Limited financial support is available. If you need support, please add a request on your registration webform with a brief justification. Please note that the workshop is relatively local in scope, so that we might be able to cover your accommodation but probably not your travel expenses.
Conference dinner
The conference dinner will be on Thursday evening at 18:00h in the atrium of the Max Planck Institute.
Practical information
For practical information such as how to get to the institute and a list of hotels see here.
Last changed on 30 Jan 2014 by Christian Blohmann
Automorphic Forms Seminar AachenKoelnLilleSiegen
This is the 41st meeting of the joint FrenchGerman intercity seminar on automorphic forms. Everybody who is interested in automorphic forms is welcome. We encourage in particular young researchers to participate and to report on their work in one of our meetings. For further informations concerning this meeting please send an email to moree@mpimbonn.mpg.de or nils.skoruppa@gmail.com.
Schedule
For the abstracts click on the titles or see the list of abstracts.
Wed, 18 Dec 2013
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BonnKöln Number Theory and Physics Seminar
Special talks in honor of Günter Harder's contributions to mathematics
On Friday, March 15, 2013 the Max Planck Institute for Mathematics will organize a meeting with some lectures to honor emeritus director Professor Günter Harder's important contributions to MPIM and Mathematics. On this occasion there will be talks by two of his former students. Professor Harder will turn 75 on March 14.
Workshop on Geometry and topology of smooth 4manifolds
Galois representations and pencils of CalabiYau motives
Details
The workshop "Galois representations and pencils of CalabiYau motives" will be held at the MPIM Bonn during the week 1521 December, 2012 as part of the activity "Quantum cohomology, Frobenius manifolds and pencils of CalabiYau varieties" in 20122013.
Email: galois2012@mpimbonn.mpg.de
Organisation (in short):
The workshop will consist of three parts. On each of the days 1517 December the agenda is broken into three consecutively running seminar classes, titled as follows:
 Congruences (moderator: Neil Dummigan)
 Crystals (moderator: Richard Crew)
 Congruences sheaves/Mirror symmetry (moderator: Alessio Corti)
We meet 12PM6PM. A number of fixed talks will be given on each of these days, however, discussions and adlib talks are encouraged.
A short conference will run on 18 December. The Seminar on Algebra, Geometry and Physics will be part of the conference, with Jan Stienstra's talk on connections between number theory and physics. There will be a social event in the afternoon.
The days 1921 December are dedicated to joint work in groups. However, Thursday 20 December will start with Number Theory Seminar at 10:45. Apart from that, we will start at 11 AM and finish at 5PM on these days.
The lunchtime on workdays is at 13:00, and the institute tea is 16:00, with the exception of Friday, 21 December.
Program and abstracts
For the abstracts click on the titles or see the list of abstracts.
Sat, 15 Dec 2012
Sun, 16 Dec 2012
Mon, 17 Dec 2012
Tue, 18 Dec 2012
Wed, 19 Dec 2012
Thu, 20 Dec 2012
December 14, afternoon:
Arrival
On the next three days seminars run continuously 12:00  late afternoon, normally with one fixed talk in each seminar.
December 15, Seminars:
~12PM: Neil Dummigan: Critical values, congruences, Selmer groups
Since the seminar I am moderating is called congruences, I'll start off by explaining the possibilities for the composition factors of the reduction mod p of the type of 4dimensional Galois representation coming from a CY 3fold, and comparing these with the kinds of congruences observed by Anton Mellit, calling on him to report on observations about pairs of congruences and common values of p. This would set the scene. At some point later I could say something about how for at least one of the three kinds of such congruences, it should lead to an element of order p in some Selmer group, how that appears in the BlochKato conjecture, which then predicts the appearance of p in an Lvalue, comparing and contrasting with the cases of congruences for SaitoKurokawa lifts, and congruences connected with ptorsion on elliptic curves.
~3PM: Jan Stienstra: Formal groups associated to pencils of CalabiYau varieties.
The CartierDieudonne module of the ArtinMazur formal group (AMFG) equals the the unit root crystal in crystalline cohomology. A Laurent polynomial (LP) with reflexive Newton polytope defines CalabiYau hypersurfaces in toric varieties. There is a very concrete formula for a logarithm for a group law for the AMFG in terms of the constant terms in powers of the LP. The AMFG is a formal group over the ring of coefficients of the LP. This ring has a natural structure of a $\lambda$ring. For formal groups over $\lambda$rings Cartier's theory can be reformulated in terms of Dirichlet series. This immediately leads to congruences. The natural geometric context for Laurent polynomials is toric geometry and the natural context for their variations is GelfandKapranovZelevinsky's theory of hypergeometric functions. The aforementioned formal group law logarithm is such a GKZ hypergeometric function. This has consequences for the unit roots of Lfunctions.
~5PM: Piotr Achinger: A characterization of toric varieties in characteristic p
A theorem of J. F. Thomsen states that Frobenius pushforwards of line bundles on smooth toric varieties are direct sums of line bundles. Using characterization of toric varieties in terms of their Cox rings, we show that this property in fact characterizes smooth projective
toric varieties.
December 16, Seminars:
~12PM: Richard Crew: Introduction to Fisocrystals on the line
We will review basic properties of Fisocrystals on a smooth variety, with particular attention to the case of an open subset of the projective line. Topics: convergence conditions, Dwork's trick, the slope filtration, and the local monodromy theorem and its applications. If time permits we will discuss Lauder's work on the explicit computation of Frobenius matrices, and Katz's congruence formulas for the Frobenius of a curve.
~3PM: Francesco Baldassarri: Loggrowth and Frobenius slope filtrations.
Convergence polygons, loggrowth polygons and Frobenius slope filtrations will be explained.
~5PM: Lucia di Vizio: Galois theory of differential equations with an action of an endomorphisms.
I'll explain how one can construct a Galois theory for differential equations that takes into account the action of a difference operator,i.e., an endomorphisms, on the solutions.The theory attaches a group scheme to a differential equation, which encodes the algebraic difference relations among the solutions of the differential equation. This is typically the case of padic differential equation with a Frobenius structure. This is a joint work with C. Hardouin and M. Wibmer.
December 18, Conference
10:0010:50 Lucia Di Vizio, Introduction to Frobenius in qdifference equations.
11:0011:50 Alexei Panchishkin, TBA
12:0012:50 Guenter Harder Modular construction of mixed motives and congruences
I will briefly describe a construction of mixed (Anderson) motives for the symplectic group $GSp_2$. These mixed motives are labelled by automorphic cusp forms $f$ on $Sl_2$ and they are extensions of pure Tate motives. I will give a formula for the BettideRham extension classes. Some rather speculative arguments suggest that these motives "create" congruences between elliptic and Siegel modular forms. These congruences have been checked in experiments by Berstroem, Faber, van der Geer and Ghitza, Ryan and Sulon.
Lunch
14:0015:00 Seminar on Algebra, Geometry and Physics
Jan Stienstra (Utrecht) An amazing coincidence of formulas for the unit root part of crystalline cohomology and the density of states for physical crystals.
Certain Laurent polynomials can be viewed as discretizations of a Laplace operator with quasiperiodic boundary conditions. The eigenvalue/eigenfunction equation for this situation then describes the level sets of the Laurent polynomial. The density of states is a measure for the size of these level sets as a function of the level. It can be approximated, in yet another discretization, by counting how the points of which the coordinates are Nth roots of 1 are distributed over the various level sets. The limit as N tends to infinity is also known in number theory/algebraic geometry as the Mahler measure of the Laurent polynomial. By a simple transformation which is reminiscent of the Mellin transform the formula for the density of states becomes a formula for the formal group which describes the unit root part of the crystalline cohomology of the level sets which are then viewed as hypersurfaces in a toric variety. For real solid state physics the Laurent polynomial has to be replaced by a matrix (i.e. an endomorphism of a vector bundle) over a toric variety.
16:00 Institute tea
Social event
December 19, Joint work in groups
December 20, Joint work in groups
11.1512.15 Number theory seminar
December 21, Joint work in groups
Departure
Official closing time of MPIM at around 14:30
Hirzebruch Colloquium and Hirzebruch Lecture
The Max Planck Institute for Mathematics in Bonn mourns the death of Professor Dr. Friedrich Hirzebruch who passed away on Sunday, May 27. His 85th birthday would have been on October 17, 2012. On this occasion the University of Bonn, the Max Planck Institute for Mathematics and the University Club are holding a oneday commemorative colloquium followed by the annual Hirzebruch lecture.
Friedrich Hirzebruch was born on October 17, 1927 in Hamm, Westphalia. From 1945 to 1950 he studied mathematics in Munster and Zurich. After two years in Princeton from 1952 to 1954 he was appointed as full Professor at the University of Bonn. His research interests were in the fields of topology and geometry. For his manifold achievements Friedrich Hirzebruch received a number of awards and prizes. Among others, the Grand Merit Cross with Star of the Federal Republic of Germany, the Wolf Prize for Mathematics, the Seki Takakazu Prize, the Lomonossov Gold Medal, the Albert Einstein Medal, and the Georg Cantor Medal of the Deutsche Mathematikervereinigung. He held honorary doctorates from over 14 universities. He was member of a number of Academies of Science and of the Order pour le mérite. Professor Hirzebuch is the founding director of the Max Planck Institute for Mathematics, which he headed from 1980 to 1995. His work largely influenced the development of modern mathematics. Through his personal efforts and achievements he contributed in an essential way to the reconstruction of mathematics research in Germany after World War II.
Program:
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