Ivana Alexandrova
PhD, Mathematics, University of California, Berkeley, 2004
MA, Statistics, University of California, Berkeley, 1999
About
Research Interests
Scattering theory, semi-classical, Aharonov-Bohm effect
Grants/Funding
Simons Foundation Collaboration Grant for Mathematicians, $35 000, September 1, 2012, to August 31, 2017
NSF Grant, DMS-0801158, $149 417, June 1, 2008, to May 31, 2011
Publications
Dr. Alexandrova also serves as an editor of the Journal of Mathematics and Statistics and the International Journal of Magnetism and Electromagnetism.
Selected Publications
Semi-Classical-Fourier-Integral-Operator-Valued Pseudodifferential Operators and Scattering in a Strong Magnetic Field. Journal of Geometric Analysis, 28 (2018): 2725 -- 2767.
Resonances in Scattering by Two Magnetic Fields at Large Separation and a Complex Scaling Method, with Hideo Tamura. Advances in Mathematics, 256 (2014): 398 -- 448.
Aharonov-Bohm Effect for Resonances of Magnetic Schrödinger Operators with Potentials with Supports at Large Separation, with Hideo Tamura. Annales de l'Institut Henri Poincaré, 12 (2011): 679 -- 721.
Resonance Free Regions in Magnetic Scattering by Two Solenoidal Fields at Large Separation, with Hideo Tamura. Journal of Functional Analysis, 260 (2011): 1836 -- 1885.
Resolvent and Scattering Matrix at the Maximum of the Potential. With Jean-François Bony and Thierry Ramond. Serdica Mathematical Journal, 34 (2008): 267 -- 310. Issue Dedicated to the 65th Anniversary of Professor Vesselin Petkov.
Semi-Classical Scattering Amplitude at the Maximum of the Potential. With Jean-François Bony and Thierry Ramond. Asymptotic Analysis, 58 (2008), 57 -- 125.
Semi-Classical Wavefront Set and Fourier Integral Operators, Canadian Journal of Mathematics, 60 (2008), 241 -- 263.
The Spectral Function at the Maximum of the Potential. With Jean-François Bony and Thierry Ramond. Proceedings of the Workshop "Spectral and Scattering Theory and Related Topics," Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, (June 2007): 14 -- 26.
Semi-Classical Behavior of the Spectral Function, Proc. AMS, 134 (2006): 2295 -- 2302.
Structure of the Short Range Amplitude for General Scattering Relations, Asymptotic Analysis, 50 (2006): 13 -- 30.
Structure of the Semi-Classical Amplitude for General Scattering Relations, Comm.~PDE, 30 (2005): 1505 -- 1535.
Talks & Presentations
Resonances in Scattering by Two Magnetic Fields at Large Separation and a Complex Scaling Method
- Rochester Institute of Technology, Mathematics Colloquium, September 8, 2016
- Purdue University, Spectral and Scattering Theory Seminar, March 30, 2016
- Syracuse University, Analysis Seminar, March 25, 2016
- Pennsylvania State University, Analysis Seminar, February 26, 2016
- Brown University, Analysis Seminar, February 8, 2016
- Bulgarian Academy of Sciences, Sofia, Differential Equations Seminar, October 29, 2014
- Mathematics Days in Sofia, Bulgaria, July 7 to 10, 2014
- University at Albany, Physics Colloquium, April 4, 2014
- UCLA, Analysis and PDE Seminar, November 8, 2013
- Stanford University, Analysis and PDE Seminar, November 7, 2013
- San Jose State University, Mathematics Colloquium, November 6, 2013
- U de Paris Nord, France, Groupe de travail Analyse semi-classique & Physique mathématique, July 1, 2013
- I Henri Poincaré, Paris, France, Trimester "Variational & Spectral Methods in Quantum Mechanics," May 27, 2013
- McGill University, Montreal, Canada, Analysis Seminar, March 22, 2013
- Lund U, Sweden, Mathematics Colloquium, December 4, 2012
- Mittag-Leffler I, Djursholm, Sweden, Hamiltonians in Magnetic Fields, November 13, 2012
- Fields I, Toronto, Canada, Weyl Law at 100, September 2012
Aharonov-Bohm Effect for Resonances of Magnetic Schrödinger Operators with Potentials with Supports at Large Separation
- Williams College, Department Colloquium, November 2011
- Rutgers University, Mathematical Physics Seminar, October 2011
- McGill University, Analysis Seminar, May 2011
- University at Albany, Analysis Seminar, April 2011
- University of Rochester, Analysis Seminar, March 2011
- Fields I, Analysis Working Group, Toronto, Canada, March 2011
Resonances for Magnetic Scattering by Two Solenoidal Fields at Large Separation
- University of Tokyo, Japan, Analysis Seminar, June 2010
- University of North Carolina, Chapel Hill, Analysis Seminar, April 2010
- AMS Special Session "Spectral \& Transport Properties of Schrödinger Operators," Lexington, KY, March 2010
- University at Albany, Mathematics Colloquium, February 2010
- Fields I Colloquium in Applied Mathematics, Toronto, Canada, January 2010
Infinite Semi-Classical Fourier Integral Operators and Beals's Lemma
- Workshop on Spectral Theory & Harmonic Analysis, Australian National University, Canberra, July 2009
Structure of the Scattering Amplitude for Schrödinger Operators with a Strong Magnetic Field
- Second Northeast Analysis Meeting, University at Albany, October 14, 2017
- Northeast Analysis Network Conference, University of Rochester, September 9 to 10, 2016
- University of Hyogo, Japan, Analysis Seminar, July 2009
- University of Tokyo, Japan, Analysis Seminar, June 2009
- University of Tsukuba, Japan, Analysis Seminar, May 2009
- University of Toronto, Canada, Analysis/PDE/Applied Math Seminar, March 2009
- McGill University, Canada, Analysis Seminar, March 2009
- U de Paris Nord, France, Groupe de Travail, February 23, 2009
- Banff International Research Station, Canada, Theory of Resonances Workshop, October 2008
- University of California, Berkeley, Analysis/PDE Seminar, October 13, 2008
- Second Symposium, Spectral & Scattering Theory, Recife & Serrambi, Brazil, August 11 to 22, 2008
Resolvent Estimates at the Maximum of the Potential
- Second Canada-France Congress, Montreal, Canada, June 3, 2008
- Thirty-third University of Arkansas Spring Lecture Series, PDEs in Conformal Geometry, April 11, 2008
- University of Toronto, Canada, Analysis/PDE/Applied Math Seminar, March 28, 2008
The Spectral Function at a Maximum of the Potential
- University de Bordeaux 1, France, Analysis Seminar, April 2007
- University of Toronto, Canada, Analysis/PDE/Applied Math Seminar, March 30, 2007
- U de Paris - Sud, France, Groupe de Travail, February 2007
- RIMS, Kyoto, Japan, "Spectral & Scattering Theory & Related Topics," February 5, 2007
- AMS Special Session "Scattering Theory & Wave Propagation," Fayetteville, AR, November 3, 2006
Semi-Classical Scattering Amplitude at a Maximum Point of the Potential
- University of Tsukuba, Japan, PDE Seminar, January 24, 2007
- Loughborough University, UK, Mathematics Colloquium, November 2006
- PanAm Adv. Studies I, Analysis & Probability in Quant. Physics, Santiago, Chile, July 31, 2006
- Institute for Advanced Study, "Zeta Functions All the Way" Research Seminar, May 2006
- East Carolina U (ECU), Mathematics Colloquium, May 2006
- Young Mathematicians Conf. in PDE & Dynamical Systems III, Fields I, April 28 to 29, 2006
- Fifty-seventh Sp 06 Midwest PDE Seminar, U of Illinois at Chicago, April 2006
- University of Toronto, Canada, Analysis/PDE/Applied Math Seminar, March 31, 2006
- University of Kentucky, PDE Seminar, March 2006
- AMS Special Session "Scattering & Spectral Problems in Geometry," Lincoln, NE, October 2005
Semi-Classical Behavior of the Spectral Function
- University of Tokyo, Japan, January 25, 2007
Structure of the Short-Range Amplitude for General Scattering Relations
- University of Tokyo, Japan, January 25, 2007
- Colorado State University , Mathematics Colloquium, January 30, 2006
- Purdue University , Spectral and Scattering Theory Seminar, January 27, 2006
- U de Paris-Sud, France, Groupe de Travail, May 2005
- Int'l Conf. on Diff. Eqs & Math. Physics, University of Alabama-Birmingham, March 2005
- York University , Canada, Analysis Seminar, October 2004
- University of Toronto, Canada, Analysis/PDE/Applied Math Seminar, October 4, 2004
Structure of the Semi-Classical Amplitude for General Scattering Relations
- University of Tokyo, Japan, January 25, 2007
- Fields I., Canada, Workshop "Semi-classical Theory of Eigenfunctions & PDEs," June 2004
- UCLA -- Caltech, Joint Analysis Seminar, April 2004
- Johns Hopkins University , Analysis Seminar, February 2004
- UC Berkeley (UCB), PDE Seminar, February 2004
Instruction & Advising
Courses
University at Albany, Spring 2011 to present
- PhD Level: Complex Analysis, Independent Study and Research, Introduction to Differentiable Manifolds, Introduction to Differential Geometry, Partial Differential Equations, Topics in Modern Mathematics
- Master's Level: Master's Seminar
- Undergraduate Level: Advanced Calculus I, Analysis for Applications I & II, Calculus II & III, Complex Analysis, Elementary Statistics, Honors Linear Algebra, Introduction to Differential Geometry, Linear Algebra, Ordinary Differential Equations, Precalculus, Probability for Statistics, Statistics, Topics in Statistical Inference, Vector Analysis
University of Tokyo, Summer 2009
- PhD Level: Semi-Classical Analysis and Scattering Theory, Topics course
East Carolina University, Fall 2006 to Fall 2010
- Master's Level: Functions of Several Real Variables, Ordinary Differential Equations I, Introduction to Complex Variables
- Undergraduate Level: Calculus I, Linear Algebra, Elementary Complex Variables, Introduction to Ordinary Differential Equations, Calculus III, Advanced Calculus, Calculus For Life Sciences I, Introduction to Functions
University of Toronto, Fall 2004 to Spring 2006
- Calculus for Arts and Science, Calculus for Engineering
University of California, Berkeley, Spring 1998 to Fall 2003
- Instructor: Analysis Written Math PhD Prelim Workshop
- Graduate Student Instructor:
- PhD Level: Theory of Functions of a Complex Variable, Probability Theory
- Undergraduate Level: Calculus I & II, Linear Algebra & Differential Equations, Calculus II, Introduction to the Theory of Probability, Concepts of Probability, Introduction to Statistics for Business
Furman University, Fall 1994 to Spring 1997
- Teaching Assistant: Calculus I, II, & III, computer integrated
- Grader: Precalculus
Additional Information
Awards & Honors
Experiential Teaching Award, Nomination, Spring 2019
Dr. Nuala McGann Drescher Affirmative Action/Diversity Leave Award, New York State / University University Professions (UUP), Fall 2014
College of Arts and Sciences Travel Grant, UAlbany, 2013 to 2014, $800
Invited Participant, "Variational and Spectral Methods in Quantum Mechanics'' Program, Institut Henri Poincaré, Paris, France, May 20 to July 12, 2013, Award: 7,000 euro and travel
College of Arts and Sciences Travel Grant, UAlbany, 2012 to 2013, $660
Invited Participant, "Hamiltonians in Magnetic Fields" Program, Mittag-Leffler Institute, Djursholm, Sweden, October 1 to December 15, 2012
Invited Visitor, McGill University, May 14 to 28, 2011
Sloan Foundation Fellowship, Nomination, 2010, 2009
Invited Visitor, Department of Math, University of Tokyo, Japan, June 16 to 30, 2010
Invited Visiting Fellow, Centre for Mathematics and its Applications, Mathematical Sciences Institute, Australian National University, Canberra, July 5 to 18, 2009
Invited Associate Professor, University of Tokyo, Japan, January 4 to July 31, 2009
Visitor, IHES, France, January 10 to February 28, 2009; July 20 to August 10, 2007
Member, MSRI, Berkeley, CA, October 13 to 17, 2008
College Research Award, East Carolina University, Spring 2008. A Sabbatical Semester Award.
Invited Visitor, Department of Math, U de Paris-Sud, France, January to August 2007
Invited Visitor, Department of Math, U de Bordeaux, France, April 23 to 27, 2007
Invited Visitor, Department of Math, University of Tokyo, Japan, January 22 to February 9, 2007
Invited Visitor, Department of Math, U de Paris - Sud, France, May 16 to June 15, 2005
Travel Grant, International Conference on Diff. Eqs & Math. Physics, University of Alabama-Birmingham, March 2005
Alexander Prize for Best Dissertation in Pure Mathematics, Nomination, University of California, Berkeley (UCB), May 2004
Research Assistantship, UCB, 2000, 2001 to 2002, Summer 2002, Spring to Summer 2003, Spring 2004
Phi Beta Kapa Fellowship, UCB, 2002 to 2003. Awarded to six PhD students.
One-month Invitation, Scattering Theory Program, ESI, Vienna, Austria. Spring to Summer 2001
Travel Grant, Department of Math, UCB, Spring 2001
Julia B. Robinson Fellowship, Department of Math, UCB, Spring 2001. Awarded to 10 PhD students.
First-year PhD Fellowship, Department of Statistics, UCB , 1997 to 1998. Awarded to one student per year.
DeLany Medal, Furman University (FU), May 1997. Awarded to the best senior mathematics major.
Dean's List, FU, 1993 to 1997
Invited participant, Summer Institute in the Mathematical Sciences, UCB, Summer 1996
Economics Research Fellowship, FU, Summer 1996
Phi Beta Kappa Honor Society, May 1996
Invited participant, Non-linear Wave Phenomena, Park City Mathematics Institute, Summer 1995
Invited participant, Mentoring Program for Women, IAS, May 1995
Furman Advantage Mathematics Research Fellowship, FU, Summer 1994, Summer 1995
Computational Science Prize, FU, Spring 1995. For solving a specified difficult course problem.
Pi Mu Epsilon Mathematics Honorary Society, April 1994
Phi Eta Sigma Freshman Honor Society, April 1994
Wylie Mathematics Scholarship, FU, 1993 to 1997
Goodwill Full Tuition, Room, and Board Scholarship, FU, 1993 to 1997
Kolarov Scholarship, High School for Math & Natural Sciences, Vratsa, Bulgaria, 1992 to 1993. Awarded to the two best mathematics students in the graduating class.
Scholarship, Sts Cyril & Methodius Foundation, Bulgaria & University of South Carolina (USC). One of eight Bulgarian students selected from more than 650, with a GPA above 5.5/6 after exams in English, biology, math, chemistry and physics, and an interview. Exchange program to USC, D.C. and New York City. June 16 to July 15, 1991.
Third Place, Spring National Math Competition for High School students, Bulgaria, April 1989
Service & Outreach
Presented at the New York State Master Teacher Program, UAlbany, June 4, 2016
Made a presentation titled, "Some New Old Ideas for Teaching High School Mathematics," at the University in the High School's Mathematics and Statistics Workshop, UAlbany, October 19, 2015
Featured in the Girls' Angle Bulletin, June/July 2015. Girls' Angle is a math club for girls.
Led a session of the Albany Area Math Circle, March 15, 2015