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Research

 

Publications

I am partially supported by the NSF grant DMS-1509693.

For updates on papers to come: my CV

Collaborators

Lara Anderson (Virginia Tech)
Kai-Siang Ang (Stanford)
David Baraglia (Adelaide)
Indranil Biswas (Tata Inst.)
Steve Bradlow (UIUC)

 
Jonathan Heckman (UNC)
Sebastian Heller (Tübingen)
Nigel Hitchin (Oxford)
Sheldon Katz (UIUC)
Jessica Li (Harvard)

16. Branes through finite group actions, with Sebastian Heller

arXiv:1611.00391


15. On the Brauer group of Higgs bundles and connections, with David Baraglia and Indranil Biswas.

arXiv:1609.00454

14. On the geometry of regular icosahedral capsids containing disymmetrons, with Kai-Siang Ang. 

Journal of Structural Biology (to appear)

arXiv:1608.082713

13. A geometric approach to orthogonal Higgs bundles

 arXiv:1608.00300

  

12. Higgs bundles and applications

Oberwolfach Reports, Report No. 31 (2015), 31-33 (DOI: 10.4171/OWR/2015/3)

arXiv:1603.06691

 11. Automorphisms of C^* moduli spaces associated to a Riemann surface, with David Baraglia and Indranil Biswas.

SIGMA 12 (2016), 007

Arxiv: 1508.06587 

10. Higgs bundles and exceptional isogenies, with Steve Bradlow. 

Research in the Mathematical Sciences (2016) 3:14.

Arxiv. 1508.02650

9. Monodromy of rank 2 twisted Hitchin systems and real character varieties, with D. Baraglia, 

Transactions of the American Mathematics Society (to appear)

Arxiv. 1506.00372  

8. Interface control and snow crystal growth, with Jessica Li, 

Phys. Rev. E 93, 023302, (2016)

arXiv. 1505.02042

7. An introduction to spectral data for Higgs bundles 

Lecture Note Series, IMS, NUS. (to appear)

arXiv. 1408.0333 

6. Real structures on moduli spaces of Higgs bundles, with D. Baraglia, 

Advances in Theoretical and Mathematical Physics, Vol 20, No 3, 525 – 551 

arXiv. 1309.1195 

5. Spectral data for U(m,m)-Higgs bundles, 

International Mathematics Research Notices, (2014).

arXiv. 1307.4419. 

4. Nonabelianization of Higgs bundles, with N. Hitchin,

Journal of Differential Geometry, Volume 97, Number 1 (2014), 79-89.

arXiv: 1307.0960.  

3. Higgs bundles and (A,B,A)-branes, with D. Baraglia,

Communications in Mathematical Physics, 331 3, pp 1271-1300 (2014)

arXiv: 1305.4638

 2. Spectral data for G-Higgs bundles,

DPhil thesis, University of Oxford (2013).

arXiv:1301.1981

 1. Monodromy of the SL_2 Hitchin fibration,

International Journal of Mathematics, Vol. 24 No. 2 (2013) 

arXiv:1111.2550 

0. A symplectic approach to constrained mechanical systems. 

MsC thesis (2008). (PDF file in Spanish)

Events Organized

17. 2017 (November)
Sonia Kovalevsky Day

TBA


co-organized James Unwin

16. 2017 (November) 
Two-day workshop

Current trends on spectral data for Higgs bundles III



15. 2017 (November) 
Weekend Workshop

RTG Workshop on the Geometry and Physics of Higgs bundles II


 

14. 2017 (November)
AIM Workshop

Singular Geometry and Higgs Bundles in String Theory


co-organized with Lara Anderson and Mboyo Esole.

13. 2017 (July)
Special Session of MCA2017 

Geometry and Physics of Higgs bundles


co-organized with F. Schaffhauser and R. Wentworth 

12. 2017 (May)
Birthday workshop

Geometry and Physics of augmented bundles


co-organized with B. Collier and G. Daskalopoulos.

11. 2016 (November)
Sonia Kovalevsky Day

Knots & Graphs

co-organized with James Unwin
at UIC, USA.
(PHOTOS) 

 10. 2016 (November)
Graduate workshop

Graduate day on Geometry and Topology


At the University of Illinois at Chicago, USA.
(PHOTOS

9. 2016 (October)
Weekend workshop

RTG Workshop on the Geometry and Physics of Higgs bundles


At the University of Illinois at Chicago, USA.
(PHOTOS

8. 2016 (July)
V CLAM & CLAM Session

Higgs bundles, instantons and real character varieties

co-organized with Florent Shaffhauser,
in Barranquilla, Colombia.
(PHOTOS

7. 2016 (June)
SCGP workshop

New perspectives on Higgs bundles, branes and quantization

co-organized with Lara Anderson, David Baraglia and Vivek Shende.
(PHOTOS

6. 2016 (June)
Weekend Workshop

Current trends on spectral data for Higgs bundles II

co-organized with Lara Anderson,
at SCGP, Stony Brook, USA.
(PHOTOS

5. 2015 (November)
Sonia Kovalevsky Day

Maths & Magic


co-organized with James Unwin
at UIC, USA.
(PHOTOS

4. 2015 (October) AIM Workshop

Spectral data for Higgs bundles


Co-organized with Joergen Andersen, David Baraglia, Philip Boalch
(PHOTOS

3. 2015 (September)
Weekend Workshop

Current trends on spectral data for Higgs bundles I


at AIM, San Jose, USA.
(PHOTOS

2. 2014 (November) UIUC Weekend Festival

MoSAIC Festival

Co-organized with Jayadev Athreya et al.
(PHOTOS

1. 2014 (May)
Junior Gear Retreat

GEAR Junior Retreat


Co-organized with M. Lee, S. Maloni, A. Sanders. (PHOTOS)

Visitors

18. Emily Cliff (UIUC)

April 16-17, 2017 


17Caleb Ashley (U Michigan)

March 12-14, 2017  


16. Tom Nevins (UIUC)

January 30, 2017  


15. Gabe La Nave (UIUC)

January 23-24, 2017   


14. Sara Maloni (Virginia)

January 8-9, 2017  


13. Marina Logares (Oxford)

October 21-25, 2016.  





12. Steve Rayan (Saskatchewan)

October 21-25, 2016.  


11. Jordan Watts (Boulder)

September 24-27, 2016.  


10. Jayadev S. Athreya (Seattle)

August 28-30, 2016.


9. Lara B. Anderson (Virginia Tech)

April 17-20, 2016.  


8. Michael Groechenig (Imperial)

April 13 2016  


7. Steve Bradlow (UIUC)

April 11 2016  





6. Brent Pym (Oxford)

March 7-10, 2016.  


5. Laura Fredrickson (UT Austin)

November 15-16, 2015.  


4. Pedram Hekmati (IMPA)

November 10-12, 2015.  


3. Theo Johnson-Freyd (Northwestern)

November 2 2016  


2. Brian Collier (UIUC)

September 13-15, 2015. 


1. Alan Thompson (Waterloo)

September 5-10, 2015.  

I travel both to give talks and to do reearch visits. The latter can be found in my CV. 

TALKS

2017

  1. Fall 2017, Differential Geometry seminar, University of Washington, Seattle, USA.
  2. August 2017, GEOQUANT Conference, Jutland, Denmark.
  3. August 2017, Topological and Algebraic Advances in QFT, Varese, Italy.
  4. July 30-August 3, Mini-course speaker at the third GEAR Retreat, Stanford University, USA.
  5. July 2017, Gauge theory and special geometry (MCA 2017). Montreal, Canada.
  6. June 2017, Mathematical Physics seminar, University of Heidelberg, Germany.
  7. May 2017, Higgs bundles and related topics, Nice, France
  8. May 29 2017, Mirror Symmetry Conference for Young Mathematicians, Ann Arbor, USA
  9. May 22 2017, Topology Seminar, Northwestern University, USA.
  10. April 2-8 2017, Mini-course mentor at the British Isles Graduate Workshop Higgs bundles, UK.
  11. March 27-31 2017, BUNDLES, TIFR, Mumbai, India.
  12. March 24-27 2017, School on Geometry and Physics, Bangalore, India
  13. February 25, Fifth Annual Midwest Women in Mathematics Symposium (WIMS), Indianapolis, USA.
  14. February 14, Mathematical Physics Seminar, IMPA, Brazil.
  15. January 24, Geometric Analysis Seminar, University of Chicago, USA
  16. January 19, Mathematical Physics seminar, Purdue University, USA.
  17. January 17, Algebraic Geometry Seminar, University of Chicago, USA.

2016

  1. December 2 2016. Encuentro Rioplatense de Álgebra y Geometría, La PLata, Argentina.
  2. November 11. Colloquium, Indiana University–Purdue University Indianapolis, USA.
  3. September 12-16 2016. Hitchin70 (Madrid sectional conference), Madrid, Spain.
  4. August 19-26 2016. Mini course at the summer program of the University of British Columbia, Canada.
  5. August 4 2016, New Perspectives on Moduli Spaces in Gauge Theory, Singapore.
  6. July 2016. String-Maths, Paris, France. (Video)
  7. May 6 2016. Algebraic Geometry Seminar, National University of Buenos Aires, Argentina.
  8. April 28 2016. Geometry Seminar, University of Texas at Austin , USA.
  9. April 22-23 2016. Representation Theory, Integrable Systems and QFT, Northwestern University, USA.
  10. March 15-31, 2016. Mini Course at the Summer school at ICTS, Bangalore (Video), India.
  11. March 4, 2016. UIC Mathematics Department Colloquium, Chicago, USA.
  12. February 2016. Higgs Bundles in Geometry and Physics, Heidelberg University, Germany.
  13. January 25 2016. Geometry and Analysis Seminar, University of Oxford, UK.
  14. January 2016. Higgs bundles and Hitchin system, Centre Bernoulli, Switzerland.
  15. January 2016. Conference on Quadratic Differentials, Cape Town, South Africa. 

2008 - 2015

See HERE or CV