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Research

 

My research in Geometry as well as in other fields.

Publications

I am partially supported by the NSF grants DMS 1509693 (at UIUC),
DMS 1611835 (at UIC),
by the NSF CAREER Award 
DMS 1749013, and by the
Alexander von Humboldt Foundation

For updates on papers to come, and for appearence of my work in the media, see my CV

Collaborators

Lara Anderson (Virginia Tech)
Kai-Siang Ang (Stanford)
David Baraglia (Adelaide)
Indranil Biswas (Tata Inst.)
 Rinni Bhansali (Stanford)
Steve Bradlow (UIUC)
Mboyo Esole (Northeastern)
Laura Fredrickson (Stanford)


Jonathan Heckman (UNC)
Sebastian Heller (Tübingen)
Nigel Hitchin (Oxford)
Sheldon Katz (UIUC)
Jessica Li (Harvard)
Yuyuan Luo (PRIMES MIT)
Steve Rayan (Saskatchewan)
James Unwin (UIC)
Mengxue Yang (UIC)
Anlin Zhang (MIT-Primes) 

Publications 

35. Moduli spaces of generalized Hyperpolygons

with Steve Rayan (sbmitted). 

arXiv


34. Generalized B-opers

with Indranil Biswas and Mengxue Yang (submitted)

ArXiv


33. Minimal percolating sets for mutating infectious diseases,

with Yuyuan Luo.

Physical Review R, To appear (2020).  

ArXiv


32. Higgs bundles without geometry 

 with Steve Rayan 

Snapshots of Modern Mathematics, to appear (2020). 

ArXiv


31. Higgs bundles – recent applications,

Notices of the AMS, to appear (May 2020)

ArXiv


30. Orthogonal Higgs bundles with singular spectral curves,

with Steve Bradlow and Lucas Branco  (submitted).

ArXiv


29. Advanced topics in gauge theory: geometry and physics of Higgs bundles.

Park City Mathematics Series, AMS, to appear (2020)

ArXiv


28. A trust model for spreading gossip in social networks,

with Rinni Bhansali. 

Proceedings of the Royal Society A, to appear (2020)

arXiv


27. The phone walkers: A study of human dependance on inactive mobile devices,

with James Unwin.

Behaviour, (2018) Volume 155, Issue 5, p. 389 - 414.

arXiv


26. Modeling epidemics on d−cliqued graphs,

with Anlin Zhang.

Letters in Biomathematics (2018) Volume 5, Number 1, p. 49-69.

arXiv


25. Cayley and Langlands type correspondences for Orthogonal Higgs bundles,

with David Baraglia.

Transactions of the American Mathematics Society, Vol. 371, Num. 10, pp 7451-7492 (2019).

 arXiv


24. Singular geometry and Higgs bundles in string theory,

with Lara B. Anderson, Mboyo Esole and Laura Fredrickson

SIGMA,  14 (2018), 037, 27 pages.

arXiv


23. T-Branes at the Limits of Geometry,

with Lara Anderson, Jonathan Heckman and Sheldon Katz.

J. High Energ. Phys. (2017) 2017: 58. 

arXiv


22. Branes through finite group actions, 

with Sebastian Heller

Journal of Geometry and Physics,  Vol. 129 (2018) 279–293

arXiv


21. On the Brauer group of Higgs bundles and connections, 

with David Baraglia and Indranil Biswas.

Hitchin 70 proceedings, Oxford University Press,   Vol. 2 Oxford University Press (2018).

arXiv

20. A geometric approach to orthogonal Higgs bundles

European Journal of Mathematics, DOI: 10.1007/s40879-017-0206-9 (2017).

 arXiv

  

19. Higgs bundles and applications

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

arXiv


18. On the geometry of regular icosahedral capsids containing disymmetrons,

with Kai-Siang Ang. 

Journal of Structural Biology, Vol. 197 No. 3, pp. 340-349 (2017).

arXiv


17. Interface control and snow crystal growth,

with Jessica Li, 

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

arXiv

16. Automorphisms of C^* moduli spaces associated to a Riemann surface

with David Baraglia and Indranil Biswas.

SIGMA 12 (2016), 007.

Arxiv 

15. Higgs bundles and exceptional isogenies, 

with Steve Bradlow. 

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

Arxiv

14. Monodromy of rank 2 twisted Hitchin systems and real character varieties, 

with D. Baraglia, 

Transactions of the American Mathematics Society,  Vol. 370, Num. 8, (2018) Pages 5491-5534.

Arxiv. 1506.00372  

13. An introduction to spectral data for Higgs bundles 

Lecture Note Series, IMS, NUS,  IMS LNS Vol 65 (2017)

arXiv

12. Real structures on moduli spaces of Higgs bundles,

with D. Baraglia, 

Advances in Theoretical and Mathematical Physics, Vol 20, No 3, 525 – 551 (2015). 

arXiv

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

International Mathematics Research Notices, (2014).

arXiv

10. Nonabelianization of Higgs bundles, 

with N. Hitchin,

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

arXiv

9 Higgs bundles and (A,B,A)-branes,

 with D. Baraglia,

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

arXiv

 8. Spectral data for G-Higgs bundles,

DPhil thesis, University of Oxford (2013).

arXiv

 7. Monodromy of the SL_2 Hitchin fibration,

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

arXiv

Popular press articles

6. Twelve Mathematical Strolls. 

with James Unwin.


5. Mathematics in the sea.  

with James Unwin.

AWM Newsletter,Volume 49, No. 6.


4. Sonia Kovalevsky Days, the potential to inspire.

with James Unwin.

AWM Newsletter. Volume 49, No. 5.

arXiv


3. Bridges between worlds, from past to present 

 AIMatters 2016,

Newsletter of the American Institute of Mathematics (2016).


2. Sonia Kovalevsky Days in Chicago,

with James Unwin.

AWM Newsletter, Volume 46 No. 6. (2016).


1. A symplectic approach to constrained mechanical systems. 

MsC thesis (2008). (in Spanish)

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

TALKS

Talks for 2020 are planned contingent on health recovery.
Due to health reasons, all non-local talks have 
been cancelled / declined since early 2019.

 

2020 

1. August 2020,   (Mini-Course) Lecture Series at Summer School in Amherst, Amherst, USA.

2. July 2020,  (Mini-Course) Undergraduate geometry & topology workshop, Notre Dame, USA.

3. July 2020, (Colloquio) FaMaF, Universidad Nacional de Cordoba, Argentina. 

3. July 2020, CLAM 2020 Diferential Geometry Session, Montevideo, Uruguay.

4. June 2020, Geometric and Analytic aspects of moduli spaces of Higgs bundles, Strasbourg, France.

5. April 2020,  Index Theory and Lie Groups, Fields Institute, Canada. 

2019 

Spring at SCGP and Fall at MSRI
  1. August 2019, Connections for Women: Holomorphic Differentials, MSRI, USA 
  2. July 2019, (Mini-Course) IAS/Park City Mathematics Institute (PCMI) 2019 Program  Park City, USA.
  3. May 2019,  Algebraic geometry seminar, Stony Brook University.
  4. April 2019, Geometry and Physics, Rutgers New Brunswick, USA
  5. April 2019, (Colloquium) Rutgers University - Newark Campus, USA.
  6. March 2019, (Colloquium) Stony Brook University, Stony Brook, USA.
  7. February 2019, (Colloquium) Simons Center for Geometry and Physics, Stony Brook, USA
  8. February 2019, Holomorphic Differentials in Mathematics and Physics, SCGP, USA.

2018 

Fall on Materninity reduced duties at Oxford

  1. November 2018, Algebraic geometry seminar, Imperial College, UK.
  2. November 2018, Algebraic geometry seminar, University of Oxford, UK.
  3. October 2018, String Theory seminar, University of Oxford, UK.
  4. June 23 2018, Workshop on the Geometry and Physics of Higgs bundles III, UIC, USA.
  5. May 22 2018, University of Oxford (seminar), Oxford, UK. 
  6. May 7 2018,  Geometry and Quantization seminar, Institut Henri Poincaré, Paris, France.
  7. April 25 2018,  Geometry seminar, University College London/King's College London, London, UK.
  8. April 7 2018, Southeastern regional mathematical string theory meeting, Duke University, USA.  
  9. March 9 2018, University of Cambridge (DAMPT & DPMMS seminar), Cambridge, UK. 
  10. January 25 2018, Northeastern University (Colloquium), Massachusetts, USA.
  11. January 23 2018, Iberoamerican Congress on Geometry (Plenary Talk), Valladolid, Spain.
  12. January 18 2018, University of Notre Dame  (Colloquium), Indiana, USA.
  13. January 16 2018, University of Washington (Colloquium), Seattle, USA.
  14. January 9 2018, University of Utah  (Colloquium), Utah, USA.
  15. January 8 2018, Max Dehn Seminar, Utah, USA.

2017

  1. November 28 2017, GEAR seminar, University of Illinois at Urbana Champaign, USA.
  2. November 9 2017, Felix Klein seminar, University of Notre Dame, USA.
  3. October 19 2017, Seminar at IST, Vienna, Austria. 
  4. October 16 2017, Mathematical Physics seminar, University of Heidelberg, Germany.
  5. October 11 2017, Higher Differential Geometry seminar, MPI, Bonn, Germany.
  6. September 1 2017, The Analysis of Gauge-Theoretic Moduli Spaces, Banff, Canada.
  7. August 15 2017, Harmonic Maps, Higgs Bundles and Integrable Systems, Hannover, Germany.
  8. August 8 2017, GEOQUANT Conference, Jutland, Denmark.
  9. August 3 2017, Topological and Algebraic Advances in QFT, Varese, Italy.
  10. July 30-August 1, GEAR Retreat (Mini-Course), Stanford University, USA.
  11. July 25 2017, Gauge theory and special geometry, MCA 2017, Montreal, Canada.
  12. July 17 2017, Geometry Seminar, FU Berlin, Germany.
  13. June 22 2017, Center for Mathematical Physics (Colloquium), Hamburg, Germany.
  14. June 12 2017, Workshop on Moduli theory & Derived category, SNU, Seoul, South Korea.
  15. June 6 2017, Mathematics - String Theory seminar, Kavli IPMU, Japan.
  16. June 1 2017, Higgs bundles and related topics, Nice, France.
  17. May 11 2017, National University of La Plata (Colloquium), La Plata, Argentina.
  18. May 29 2017, Mirror Symmetry Conference for Young Mathematicians, Ann Arbor, USA
  19. May 22 2017, Topology Seminar, Northwestern University, USA.
  20. April 2-8 2017, British Isles Graduate Workshop Higgs bundles  (Mini-Course mentor), UK.
  21. March 27-31 2017, BUNDLES, TIFR, Mumbai, India.
  22. March 24-27 2017, School on Geometry and Physics, Bangalore, India.
  23. February 25 2017, Fifth Annual Midwest Women in Mathematics Symposium (WIMS), Indianapolis, USA.
  24. February 14 2017, Mathematical Physics Seminar, IMPA, Brazil.
  25. January 24 2017, Geometric Analysis Seminar, University of Chicago, USA
  26. January 19 2017, Mathematical Physics seminar, Purdue University, USA.
  27. January 17 2017, Algebraic Geometry Seminar, University of Chicago, USA.

2016

  1. December 2 2016. Encuentro Rioplatense de Álgebra y Geometría, La PLata, Argentina.
  2. November 11. Indiana University–Purdue University Indianapolis (Colloquium), USA.
  3. September 12-16 2016. Hitchin70, 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

Visitors

 2020 (TBA)


32. Steve Rayan, (University of Saskatchewan)

April 26 - May 1, 2020


31. Ingmar Saberi, (Universität Heidelberg)

April 12-19, 2020


30. Nikita Nikolaev, (Université de Genève)

March 29-31, 2020


29. Maggie Miller, (Princeton University)

March 15-17, 2020

2019


Spring:  Visitors through my semester-long program at the Simosn Center for Geometry and Physics


http://scgp.stonybrook.edu/archives/24984

2018


28.  Sebastian Schulz, (UT Austin)

June 22 - Jully 8, 2018


27. Simon Pepin (FU Berlin)

March 12-18, 2018.


26. Victoria Hoskins (FU Berlin)

March 12-21, 2018.


25. Ben Davison (Glasgow)

March 3-6, 2018.


24. Maxime Bergeron (U Chicago)

February 26, 2018.


23. Marco Guaraco (U Chicago)

February 19, 2018

2017


22. Daniele Alessandrini (Heidelberg)

November 10-17, 2017.


21. Camilla Felisetti (Bologna)

November 9-17, 2017.


20. Steven Rayan (Saskatchewan)

November 11-15, 2017.


19. Emily Cliff (UIUC)

April 16-17, 2017.


18. Nathan Clemen (Wisconsin)

April 10, 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.  




2016


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.  


2015


5. Laura Fredrickson (UT Austin)

November 15-16, 2015.  


4. Pedram Hekmati (IMPA)

November 10-12, 2015.  


3. Theo Johnson-Freyd (Northwestern)

November 2 2015.  


2. Brian Collier (UIUC)

September 13-15, 2015. 


1. Alan Thompson (Waterloo)

September 5-10, 2015.