Curriculum Vitae

Robert Castellano Email: [email protected]

Columbia University Department of Mathematics 2990 Broadway Room 509, MC 4406 New York, NY 10027

Fax: (212) 854-8962

Office: Mathematics 408

math.columbia.edu/∼castellano

Phone: (212) 854-5886

Research Interests

I am interested in symplectic geometry and topology. I am studying problems related to regularization techniques for moduli spaces of J-holomorphic curves, specifically Kuranishi atlases and their relation to other techniques. I am also interested in computational methods in symplectic geometry, including numerically estimating symplectic capacities and symplectic embeddings.

Education

Columbia University Ph.D. in Mathematics, expected May 2016 Advisor: Dusa McDuff Thesis: Genus zero Gromov-Witten axioms via Kuranishi atlases M.Phil. in Mathematics, October 2014 M.A. in Mathematics, February 2013

2011-Present

Stony Brook University B.S. in Mathematics, May 2011 Summa Cum Laude Departmental Honors

2007-2011

Publications and Genus zero Gromov-Witten axioms via Kuranishi atlases, in preparation. Prepints Smoothness of Kuranishi atlases on Gromov-Witten moduli spaces, arXiv:1511.04350. Teaching

Columbia University Department of Mathematics • Designed and led an undergraduate seminar Topic: Enumerative geometry and string theory

Fall 2015

• Instructor Mathematics V1101, Calculus I

Spring 2015

• Teaching Assistant Mathematics W4041, Intro to Modern Algebra I • Instructor Mathematics V1101, Calculus I

Fall 2014 Spring 2014

• Teaching Assistant Mathematics W4041, Intro to Modern Algebra I

Fall 2013

• Teaching Assistant Mathematics S1201, Calculus III

Summer 2013

• Teaching Assistant Mathematics S2010, Linear Algebra

Summer 2013

• Teaching Assistant Mathematics V1201, Calculus III

Spring 2013

• Teaching Assistant Mathematics V1101, Calculus I

Fall 2012

• Teaching Assistant Mathematics S1101, Calculus I

Summer 2012

• Teaching Assistant Mathematics S1202, Calculus IV

Summer 2012

Stony Brook University Department of Mathematics

Talks and Presentations

• Lecturer MAP 103, Proficiency Algebra

Fall 2010

• Teaching Assistant MAT 123, Introduction to Calculus

Fall 2009

Making cobordisms symplectic Columbia Symplectic Topology Preprint Seminar

September 2015

Recent developments in displacement energy Columbia Symplectic Topology Preprint Seminar

February 2015

Introduction to Gromov-Witten invariants Columbia Undergraduate Mathematics Society

October 2014

Hochschild cohomology Columbia Categorical Dynamics Seminar

September 2014

Orderability in contact topology New Advances in Symplectic and Contact Flexibility Workshop Gromov’s pseduoholomorphic curve techniques Graduate Student Math Conference, Brown University

March 2014

Algebro-geometric techniques in symplectic geometry Columbia Graduate Student Seminar

February 2014

Morse-Bott homology with an eye towards pseudoholomophic curves Columbia Fundamentals of Contact Homology Seminar

November 2013

Cobordism maps in contact homology and Hutchings’ obstruction Columbia Fundamentals of Contact Homology Seminar

October 2013

Various talks Columbia Informal Symplectic Geometry Seminar

2013-Present

Various talks Columbia Graduate Student Topology Seminar Academic Honors

May 2014

2012-2014

NSF Graduate Research Fellowship Honorable Mention

2013

Faculty Fellow at Columbia University

2011-Present

Department of Mathematics Banner Bearer

May 2011

Provost Award for Academic Excellence

May 2011

Stony Brook Foundation Award for Excellence in Mathematics

May 2010

Goldwater Scholarship Honorable Mention Phi Beta Kappa Undergraduate Research and Creativity Travel Grant Bio SIGMAA Janet L. Anderson Prize for

2010 Elected May 2010 January 2010 MathFest, August 2009

Undergraduate Research in Mathematical or Computational Biology Conferences and Workshops Attended

Summer School on Moduli Problems in Symplectic Geometry, IHES, Paris, France Computational Symplectic Geometry, Tel Aviv University and ICERM, Providence, RI

July 2015

May-August 2015

Graduate Student Topology and Geometry Conference, University of Illinois at Urbana-Champaign

March 2015

Great Lakes Geometry Conference, University of Michigan, Ann Arbor

March 2015

SFT VII - Function Theory on Symplectic Manifolds, Westf¨ alische Wilhelms-Universit¨at M¨ unster

August 2014

Workshop on Contact Geometry in Dimension Three and Higher, University College London

July 2014

Workshop on Moduli Spaces of Pseudo-holomorphic Curves II, Simons Center for Geometry and Physics

June 2014

New Advances in Symplectic and Contact Flexibility Workshop, Asilomar, CA

May 2014

Great Lakes Geometry Conference, Universtiy of Notre Dame

April 2014

Graduate Student Topology and Geometry Conference, University of Texas at Austin

April 2014

Workshop on Moduli Spaces of Pseudo-holomorphic Curves I, Simons Center for Geometry and Physics Workshop on the Topology and Invariants of Smooth 4-Manifolds, University of Minnesota, Twin Cities Topology, Symplectic and Contact Geometry in Toulouse, Universit´e Paul Sabatier - Toulouse III • Introductory week

March 2014

August 2013

June 2013

• GESTA (Geometria Simpl´ectica con T´ecnicas Algebraicas) week • La Llagonne summer school on Donaldson hypersurfaces • Low-dimensional Topology and Geometry in Toulouse on the occasion of Michel Boileau’s 60th birthday Workshop on J-holomorphic Curves in Symplectic Geometry, Topology, and Dynamics, Centre de recherches math´ematiques, Universit´e de Montr´eal Graduate Student Topology and Geometry Conference, University of Notre Dame

April-May 2013

April 2013

Symplectic and Low Dimensional Topologies in Interaction, Simons Center for Geometry and Physics

December 2012

Graduate Workshop on Symplectic and Contact Topology, Simons Center for Geometry and Physics

October 2012

Panorama of Topology: A Conference in Honor of William Browder, Princeton University Indiana University Graduate Student Topology Conference, Indiana University Relevant Work

May 2012

March 2012

Department of Defense • Worked as an applied research mathematician.

Summer 2011

• Mathematically analyzed a cryptologic to determine appropriate key management techniques for the system. • Published internal paper on the analysis of the cryptologic. Stony Brook University Honors Thesis Advisors: Moira Chas and Dennis Sullivan Thesis: Geodesics on Hyperbolic Surfaces

Spring 2010-Spring 2011

Grand Valley State University NSF Research Experience for Undergraduates, Allendale, MI Advisor: Edward Aboufadel • Investigated the applications of wavelets to type I diabetes.

Summer 2009

• Developed a new measurement to quantify the variability of a diabetic’s blood sugar. • Results published in Algorithms. • Presented research at two national conferences. Activities

Mentor for Columbia Symplectic Geometry REU Topic: Obstructions of Symplectic Embeddings Co-organizer of Columbia University Graduate Student Seminar Mentor for Columbia Contact Geometry REU Topic: Reeb Dynamics of Lens Spaces Department of Mathematics Graduate Student Representative Advised Undergraduate Reading Course in Symplectic Geometry Instructor for Science Honors Program Course: Geometry and Topology Co-organizer of Columbia University Informal Symplectic Geometry Seminar Co-organizer of Columbia University Graduate Student Topology Seminar

Summer 2015

Fall 2014 Summer 2014

2014 - Present Spring 2014 Fall 2012

2013-Present

2012-2013

Mathematics Editor of Young Investigators Review, Stony Brook University Languages

English: Native French: Basic Russian: Basic

Programming

Prior work experience with: C++, Maple, Mathematica, Perl.

2009-2011