Organizers: Richard Wentworth (Math), Tristan Hubsch (Physics, Howard Univ.), Jonathan Rosenberg (Math), Amin Gholampour (Math, on leave fall 2018)
Other Faculty Participants: Joel Cohen (Math, on leave fall 2018), Paul Green (Math, emeritus)
When: Thursdays @ 3:30pm-4:30pm
Where: PHY 1117 changed to MTH 1308 effective 9/27/18

This interdisciplinary RIT will aim to foster interactions between mathematicians and physicists on topics of mutual interest.  It will roughly follow the example of a similar RIT from 2010-2011 and from the last three years. The topic for 2016-17 was mirror symmetry.  Topics for 2017-2018 were topological states of matter (fall) and generalized geometry (spring).

It is not assumed that participants already be knowledgeable in both math and physics, just in some aspect of one or the other. Relevant math topics are differential geometry, representation theory, algebraic topology, and algebraic geometry. Relevant physics topics are classical and quantum field theories, and supersymmetry.

The organization meeting for Fall 2018 is scheduled for September 6th. Students (advanced undergraduates or graduate students) who want to participate can get credit as MATH 489 (undergrad) or 689 (graduate) if they wish, by contacting the organizers.

We have a wiki where participants can exchange comments and revise notes.  Contact the math/physics computer helpdesk if you need a login id and password.

### Topics and references for 2018-2019

The topic for fall 2018 is the AdS/CFT correspondence. Here is a list of references to get started:

1. Juan Maldacena, The gauge/gravity duality, arXiv:1106.6073.
2. Horatiu Nastase, Introduction to AdS-CFT, arXiv:0712.0689.
3. Makoto Natsuume, AdS/CFT Duality User Guide, arXiv:1409.3575.
4. Sean A. Hartnoll, Andrew Lucas, Subir Sachdev, Holographic quantum matter, arXiv:1612.0732.
5. Davide Gaiotto, Juan Maldacena, The gravity duals of N=2 superconformal field theories, arXiv:0904.4466.
6. O. Aharony, S.S. Gubser, J. Maldacena, H. Ooguri, Y. Oz, Large N Field Theories, String Theory and Gravity, arXiv:hep-th/9905111.
7. Juan Maldacena, The Large N limit of superconformal field theories and supergravity, arXiv:hep-th/9711200.
8. James Lindesay and Leonard Susskind, The Holographic Universe, World Scientific, 2004.
9. Jonas Probst, Applications of the Gauge/Gravity Duality, Ph.D. thesis, Oxford, 2018.
10. Raman Sundrum, From Fixed Points to the Fifth Dimension, arXiv:1106.4501.
11. Vladimir Rosenhaus, An introduction to the SYK model, arXiv:1807.03334.
12. Gábor Sárosi, AdS2 holography and the SYK model, arXiv:1711.08482.

The topic for spring 2019 is Bridgeland stability. We will start with a little background on algebraic geometry and the physics motivation, and then give a quick introduction to triangulated categories, before getting to the main topic.  Here is a list of references to get started:

1. Emanuele Macrì and Benjamin Schmidt, Lectures on Bridgeland Stability, arXiv:1607.01262.
2. Emanuele Macrì and Paolo Stellari, Lectures on non-commutative K3 surfaces, Bridgeland stability, and moduli spaces, arXiv:1807.06169.
3. François Charles, Conditions de stabilité et géométrie birationnelle [d'après Bridgeland, Bayer-Macrì, ...] (Bourbaki talk), arXiv:1901.02930.
4. Arend Bayer, A tour to stability conditions on derived categories (lecture notes).
5. Ciaran Meachan, Moduli of Bridgeland-Stable Objects, PhD thesis, Univ. of Edinburgh, 2012.
6. Claudio Fontanari and Diletta Martinelli, Why should a birational geometer care about Bridgeland stability conditions?, arXiv:1605.04803.
7. Dominic Joyce, Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow, arXiv:1401.4949.
8. Daniel Huybrechts, Introduction to stability conditions, arXiv:1111.1745.
9. Tom Bridgeland, Spaces of stability conditions, arXiv:math/0611510.
10. Maxim Kontsevich and Yan Soibelman, Stability structures, motivic Donaldson-Thomas invariants and cluster transformations, arXiv:0811.2435
11. Tom Bridgeland, Stability conditions on triangulated categories, Ann. of Math. (2) 166 (2007), no. 2, 317-345.
12. Michael R. Douglas, D-branes, categories and 𝒩=1 supersymmetry, J. Math. Phys. 42 (2001), no. 7, 2818–2843.
13. Tom Bridgeland and Ivan Smith, Quadratic differentials as stability conditions, Publ. Math. Inst. Hautes Études Sci. 121 (2015), 155–278.

### Topics and references for 2017-2018

The topic for fall 2017 is topological states of matter. In no particular order, here is a list of references:

1. Emil Prodan and Hermann Schulz-Baldes, "Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics", arXiv:1510.08724.
2. Daniel Freed and Greg Moore, Twisted equivariant matter, Ann. Henri Poincaré 14 (2013), no. 8, 1927–2023, arXiv:1208.5055.
3. A. Kitaev, Periodic table for topological insulators and superconductors. AIP Conf. Proc. 1134, 22–30 (2009). doi:10.1063/1.3149495, arXiv:0901.2686
4. F.D.M. Haldane, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the "parity anomaly". Phys. Rev. Lett. 61, 2015–2018 (1988).
5. C.L. Kane and E.J. Mele, Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005), arXiv:cond-mat/0411737
6. C.L. Kane and E.J. Mele, Z2 Topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005), arXiv:cond-mat/0506581.
7. C.L. Kane and E.J. Mele, Topological Mirror Superconductivity, Phys. Rev. Lett. 111, 056403 (2013), arXiv:1303.4144.
8. Jean Bellissard, Noncommutative Geometry and the Quantum Hall Effect, Proceedings of the International Conference of Mathematicians (Zürich 94), Birkhäuser (1995).
9. J. Bellissard, A. van Elst, H. Schulz-Baldes, The Non Commutative Geometry of the Quantum Hall Effect (longer version of #8 above), arXiv:cond-mat/9411052.
10. David Tong: Lectures on the Quantum Hall Effect, Univ. of Cambridge, arXiv:1606.06687.
11. Edward Witten, Three Lectures On Topological Phases Of Matter, arXiv:1510.07698.
12. Ralph M. Kaufmann, Dan Li, and Birgit Wehefritz-Kaufmann, Notes on topological insulators, Rev. Math. Phys., 28(10), 1630003, 2016, arXiv:1501.02874.
13. Anton Akhmerov, Jay Sau, et al., Topological condensed matter, an online course.

The topic for spring 2018 is generalized geometry and its applications to physics (especially supersymmetry and string theory). We will begin with the first reference listed, Hitchin's notes. Here is a short list of basic references:

1. N. Hitchin, Lectures on Generalized Geometry, arXiv:1008.0973.
2. M. Zabzine, Lectures on Generalized Complex Geometry and Supersymmetry, arXiv:hep-th/0605148.
3. Dimitrios Tsimpis, Generalized geometry lectures on type II backgrounds, arXiv:1606.08674.
4. N. Hitchin, Generalized Generalized Calabi-Yau manifolds, Q. J. Math. 54 (2003), no. 3, 281–308, arXiv:math/0209099.
5. M. Gualtieri, Generalized Kahler geometry, arXiv:1007.3485.
6. G. Cavalcantri and M. Gualtieri, Generalized complex geometry and T-duality, arXiv:1106.1747.

### Topics from previous years:

1. Supermanifolds, topology, and integration --- a few references:
• S. J. Gates, Ectoplasm has no topology, hep-th/9709104 and hep-th/9809056.
• E. Witten, Notes On Supermanifolds and Integration1209.2199.
• The Berezin integral.
• S. J. Gates and G. Tartaglino-Mazzucchelli, Ectoplasm and superspace integration measure for 2D supergravity with four spinorial supercurrents, 0907.5264.
• S. J. Gates and A. Morrison, A Derivation of an Off-Shell N = (2,2) Supergravity Chiral Projection Operator, 0901.4165.
2. Dimensonal reduction in supersymmetry
• For example, S. J. Gates and T. Hubsch, On dimensional extension of supersymmetry: From worldlines to worldsheets, 1104.0722, deals with reduction from 1+1 to 0+1 dimensions.
3. Adinkras and combinatorics--- a few references:
• Yan Zhang, The combinatorics of adinkras.
• Yan Zhang, Adinkras for mathematicians, 1111.6055.
• Greg Landweber, Bibliography on adinkras.
• C. Doran, K. Iga, G. Landweber, and S. Mendez-Diez, Geometrization of N-extended 1-dimensional supersymmetry algebras, 1311.3736.
• T. Hübsch and G.A. Katona, On the Construction and the Structure of Off-Shell Supermultiplet Quotients, Int. J. Mod. Phys. A27 (2012) 1250173, 1202.4342.
• C.F. Doran, T. Hübsch, K.M. Iga and G.D. Landweber,  On General Off-Shell Representations of Worldline (1D) Supersymmetry, Symmetry 6 no. 1, (2014) 67–88, 1310.3258.
4. Super-Riemann surfaces and physical applications
5. The Haag-Łopuszański-Sohnius Theorem and its variants. This is the supersymmetric analogue of the better-known Coleman-Mandula Theorem.
6. Mirror symmetry (2016-2017).  In the fall, we followed a somewhat ad hoc approach based on looking at a lot of examples (e.g., elliptic curves and the quintic Calabi-Yau).  In the spring, we followed the multi-author book published by AMS, Dirichlet Branes and Mirror Symmetry.  The preface and Chapter 1 can be downloaded from the AMS website; Chapter 2 is at arXiv:hep-th/0609042.  An electronic version of the whole book is available at http://www.claymath.org/publications/online-books

### Detailed schedule posted below.

Organizers: Ricardo Nochetto, Wujun Zhang
When: Wednesdays @ 5pm-6pm, starting the first week of February
Where: room TBA
Subtitle: PDE theory and numerical analysis

Fully nonlinear second order elliptic PDEs arise naturally from differential geometry, stochastic control theory, optimal transport and other fields in science and engineering. In this RIT, we will discuss the concept of viscosity solutions and regularity theory of these PDEs. Some possible topics include:

• fully nonlinear elliptic equations and viscosity solutions
• Alexandroff-Bakelman-Pucci estimates
• Harnack inequality and Hölder regularity
• Uniqueness of solutions
• W2,p estimates
• C1, α estimates
• C2, α estimates

In contrast to an extensive PDE literature, the numerical approximation reduces to a few papers. We would like to discuss some criteria for designing convergent numerical methods and some tools developed recently which are useful to obtain rates of convergence. Some possible topics include:

• criterion for convergence of numerical methods
• discrete version of the Alexandroff-Bakelman-Pucci estimate
• finite element method for linear elliptic equations in non-divergence form
• numerical method for Monge-Ampere equations

Organizers: Niranjan Ramachandran, Dio Margetis, and Leo Koralov
When:
Wednesday @ 3:15pm, Tea 2:45pm - 3:15 pm in room 3201
Where:
Math 3206
From time to time special colloquia are held on other days, sometimes as part of conferences.
Other special colloquia are the Aziz Lectures and Avron Douglis Memorial Lectures.

Location: Math 3206
Day: Wednesday (with occasional talks Friday)
Time: 3:15pm
Tea: 2:45pm in 3201
Organizers: Giovanni Forni, Harry Tamvakis, Konstantina Trivisa

## 2011 - 2012 Colloquium Schedule

#### Sept 14

Wonderful compactifications of groups as moduli spaces of principal bundles

#### Sept 28

An introduction to essential dimension
Patrick Brosnan(University of Maryland),

#### Oct 21

Rigidity of group actions, cohomology and compactness
David Fisher (Indiana University, Bloomington),

#### Oct 28

A Filtration of Open/Closed Topological Field Theory
Ezra Getzler (Northwestern University),

#### Nov 2

Rational billiards and the SL(2,R) action on moduli space
Alex Eskin (University of Chicago),

#### Nov 9

Why and how do we use wavelets to study turbulence?
Marie Farge(Directrice de Recherche CNRS)

#### Nov 16

Mixed volume computation and solving polynomial systems
Tien-Yien Li (Michigan State University),

#### Dec 2

Optimal and Practical Algebraic Solvers for Discretized PDEs - Aziz Lecture
Jinchao Xu (Pennsylvania State University),

#### Dec 7

DMS to THRIVE
Sastry G. Pantula(National Science Foundation)

#### Feb 8

On the rigidity of black holes - Douglis Lecture
Sergiu Klainerman(Princeton University )

#### Feb 17

Product formulas for positive measures and applications - February Fourier Talks
Peter Jones(Yale University),

#### Feb 22

Semismooth Newton Methods: Theory, Numerics and Applications - Aziz Lecture
Michael Hintermüller (Humboldt University, Berlin),

#### Feb 29

On the size of the Navier - Stokes singular set
Walter Craig (McMaster University),

#### Mar 14

De Giorgi methods applied to regularity issues in Fluid Mechanics
Alexis Vasseur (UT Austin )

#### Mar 30

Birkhoff Normal Form and a problem of Herman - Dynamics Conference
Hakan Eliasson (University of Paris-6 and IAS),

#### Apr 25

Lyapunov Functions: Towards an Aubry-Mather theory for homeomorphisms?
Albert Fathi (ENS-Lyon),

#### May 2

Contractions of Lie Groups and Representation Theory
Nigel Higson (Penn State University), cancelled

#### May 9

The Pfaffian-Grassmannian Derived Equivalence
Andrei Caldărăru (University of Wisconsin, Madison),

This area includes information on research done in the department, seminars and conferences hosted by the department, as well as access to electronic research resources.

### Subcategories

Archives: 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019

• #### Speaker: Benjamin Kedem (UMD) - https://www.math.umd.edu/~bnk/

When: Wed, September 5, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Lloyd N. Trefethan (Oxford University)

When: Wed, September 12, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Dan Ciubotaru (University of Oxford) - https://www.maths.ox.ac.uk/people/dan.ciubotaru

When: Wed, September 19, 2018 - 3:15pm
Where: Chemical Engineering Room 2110
• #### Speaker: Michael Rapoport (UMD and University of Bonn) - http://www.math.uni-bonn.de/ag/alggeom/rapoport

When: Wed, September 26, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Marsha Berger (NYU) - https://cs.nyu.edu/berger/

When: Wed, October 3, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Alan Frieze (CMU) - https://www.math.cmu.edu/~af1p/

When: Fri, October 5, 2018 - 11:00am
Where: CSIC 2117
• #### Speaker: Christoph Ortner (University of Warwick) - https://warwick.ac.uk/fac/sci/maths/people/staff/christoph_ortner/

When: Tue, October 9, 2018 - 11:00am
Where: Kirwan Hall 3206
• #### Speaker: Department meeting () -

When: Wed, October 10, 2018 - 3:15pm
Where: Kirwan Hall 3206

When: Fri, October 12, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Department meeting () -

When: Wed, October 17, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Helge Holden (NTNU (Norwegian University of Science and Technology)) - https://www.ntnu.edu/employees/holden

When: Fri, October 26, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Jianfeng Lu (Duke University) - https://services.math.duke.edu/~jianfeng/

When: Tue, October 30, 2018 - 11:00am
Where: Kirwan Hall 3206
• #### Speaker: Jeff Adams (UMD ) - https://www.math.umd.edu/~jda/

When: Wed, November 7, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Department meeting () -

When: Wed, November 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Dr. Scott ArmstrongAbstract: I will discuss the large-scale asymptotics of solutions of linear elliptic equations with random coefficients. It is well-known that solutions converge (in the limit of scale separation) to those of a deterministic equation, a kind of law of large numbers result called "homogenization". In recent years obtaining quantitative information about this convergence has attracted a lot of attention. I will give an overview of one such approach to the topic based on variational methods, elliptic regularity, and renormalization-group'' arguments.

When: Wed, November 28, 2018 - 3:15pm
Where: 3206 William E. Kirwan Hall
• #### Speaker: Otis Chodosh (Princeton University) - https://web.math.princeton.edu/~ochodosh/

When: Wed, December 5, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Joshua Cape (Johns Hopkins University) -

When: Fri, December 14, 2018 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Yiqiao (Joe) Zhong (Princeton University) -

When: Fri, January 4, 2019 - 11:00am
Where: Kirwan Hall 3206
• #### Speaker: Zhenhua Lin (University of California -- Davis) -

When: Mon, January 7, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Xueying Tang (Columbia University) -

When: Wed, January 9, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Vince Lyzinski (U-Mass Amherst) -

When: Fri, January 11, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Mengyang Gu (Johns Hopkins University) -

When: Mon, January 14, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Rita Ferreira (KAUST, Saudi Arabia) - https://www.ritaferreira.pt/

When: Fri, January 25, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Chenyang Xu (MIT) - http://math.mit.edu/~cyxu/

When: Wed, March 13, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Jonathan Mattingly (Duke University) - https://math.duke.edu/people/jonathan-christopher-mattingly

When: Wed, April 10, 2019 - 3:15pm
Where: Kirwan Hall 3206
• #### Speaker: Ralf Hiptmair (ETH, Zurich) - https://www.math.ethz.ch/sam/the-institute/people/ralf-hiptmair.html

When: Wed, May 1, 2019 - 3:15pm
Where: Kirwan Hall 3206