Peter Kuchment

Department of Mathematics

Texas A&M University

College Station, TX 77843-3368

Voice: (979) 862-3257

FAX: (979) 862-4190

e-mail: kuchment@math.tamu.edu

Web page: http://www.math.tamu.edu/~kuchment

Field

Pure and Applied Mathematics, Math. Education

• Partial Differential Equations and Mathematical Physics

• Integral Geometry with applications to Computerized Tomography and Biomedical Imaging

• Geometric Analysis

• Photonic crystal theory.

• Quantum Graphs with applications to mathematical modeling of meso- and nano-scale structures.

• Enhancement of K-12 education

Education

Experience

Courses taught

• Introduction to Contemporary Mathematics

• Trigonometry

• Calculus Sequence

• Advanced Calculus

• Ordinary Differential Equations

• Introduction to Mathematical Biology

• Engineering Mathematics

• Complex Analysis

• Numerical Linear Algebra

• Partial Differential Equations

• Numerical Partial Differential Equations

• Functional Analysis

• Theory of Distributions and Fourier Analysis

• Topology

• Microlocal Analysis and Pseudodifferential Operators

• Computerized Tomography

• Probability and Statistics

• Classical Mechanics

• Classical Field Theory and Special Relativity

Graduate Advising

Advised on ten Ph.D. Dissertations:

1. V.Sviridov, Some problems of the theory of periodic differential equations, 1986, Voronezh, USSR. Currently an Assoc. Prof. at the Polytechnic Univ., Kursk, Russia.

2. L.Khinkis, Spectral synthesis on semi- simple Lie groups, 1987, Voronezh, USSR. Currently an Assoc. Prof. and Chair of Math. Department at Canisius College, Buffalo, NY.

3. L.Solomatina, Some problems on invariant differential equations on Riemannian symmetric spaces, 1990, Voronezh, USSR. Currently an actuary in Moscow, Russia.

4. V. Aguilar, The range of the exponential Radon transform, 1995, Wichita State University, Wichita, KS. Currently an Assoc. Professor and Chair of the Math. Dept., Univ. San Francisco de Quito, Quito, Ecuador.

5. S. Lissianoi, Mathematical problems of tomography and radiation therapy, 1996, Wichita State University, Wichita, KS. Won the 1997 Dora Wallace Hodgson Outstanding Doctor Dissertation Award and an Award for the best student presentation during a 1996 Meeting of Kansas Section of MAA. Currently at Bay Networks in Boston, MA.

6. I. Ponomarev, Numerical analysis of problems of tomography, radiotherapy, and photonic crystal theory, 1997, Wichita State University, Wichita, KS. Currently in the family oil business.

7. L. Kunyansky, Numerical and Analytic Study of Problems of Photonic Crystal Theory, 1998. Wichita State University, Wichita KS. The 1998 recipient of the Dora Wallace Hodgson Outstanding Doctoral Student Award. Currently an Associate Professor at the Math. Dept., U. Arizona, Tucson, AZ.

8. H. Zeng, Convergence of spectra of mesoscopic systems collapsing onto a graph, 2001, Wichita State University, Wichita, KS. Currently an Associate Professor at Fort Heys Univ., KS.

9. Gaik Ambartsoumian, Spherical Radon Transform and Mathematical Problems of Thermoacoustic Tomography, 2006, Texas A&M University, College Station, TX. The 2006 recipient of Guzeman Award. Starting 2006, an Assistant Prof. at Univ. of Texas, Arlington.

10. Beng-Seong Ong, Spectral Problems of Optical Waveguides and Quantum Graphs, 2006, Texas A&M University, College Station, TX. Currently at the geophysics company Veritas, Houston.

11. Yulia Georgieva-Hristova - current student, working on medical imaging.

12. Linh Nguyen - current student, working on medical imaging.

13. Moritz Allmaras - current student, working on medical imaging.

Advised on two Masters Theses:

1. A. Panchenko, John's equation and the range of the exponential Radon transform, 1996. Wichita State University, Wichita KS. Currently Assistant Prof. at Washington State Univ. after receiving a PhD from the Univ. of Delaware.

2. W. Axmann, Computations of spectra of photonic crystals, 1998. Wichita State University, Wichita KS. Currently helds PhD in Physics from Kansas State Univ. and teaches at Wichita State Univ., KS.

Masters students graduating with no thesis:

1. D. Meyers (2005)

2. E. Rodriguez (2005)

Research and Education Grants

Recent honors and awards

• Fellow of the Institute of Physics, 2009

• Paper "Tight frames of exponentially decaying Wannier functions", J. Phys. A: Math. Theor. 42 (2009) was chosen as IOP (Inst. of Physics) Select Paper. 2008

• Texas A&M Department of Mathematics Outstanding Teaching Award, 2008.

• Texas A&M Association of Former Students Tecahing Award, 2008.

• Member of Clare Hall college, University of Cambridge, 2007

• Joint paper with M. Agranovsky "Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography", Inverse Problems 23 (2007) was selected by the Editorial Board for the 2007 highlights.

• Texas A&M Department of Mathematics Outstanding Service Award, 2005.

Professional Membership

American Mathematical Society, Society for Industrial and Applied Mathematics, Mathematical Association of America, International Association of Mathematical Physics, Institute of Physics, Pi Mu Epsilon.

Professional Service

• Inverse Problems core leader and member of the Executive Committee, IAMCS (Institute ofr Applied Mathematics and Computational Science) at Texas A&M University, 2008 - present.

• Associate Editor, Bulletin of the AMS (Book Reviews), 01/2005-2012.

• Judge, SIAM student paper contest, 2008.

• Editor of five AMS volumes and one special journal issue.

• Member of the AMS Committee on Education, February 2000 - January 2003

• Co-organizer Focus group discussion, AMS Annual Meeting, New Orleans, January 2001.

• Member of the AMS Committee on Meetings and Conferences, February 2000 - January 2001

• Referee during the past several years for: Comm. Math. Phys.; Comm. PDEs; GAFA; Inverse Problems; J. Approx. Theory; J. Comput. Physics; J. Theor. Probability; J. d'Analyse; J. Fourier Analysis; J. Math. Anal. and Appl.; J. Operator Theory and Integral Equations; J. Optics; J. Physics; Medical Physics; Memoirs of the AMS; Neural, Parallel, and Scientific Computations; SIAM J. Appl. Math.; SIAM J. Math. Anal.; Transactions of the AMS; IEEE Optics Lett.; IEEE Trans. Med. Imaging; IEEE Trans. Microwave Theory and Techniques.

• Proposal reviewer and member of several panels during the past several years for NSF, DOD, DOE, SPSRC (UK analog of NSF), Isaac Newton Inst. Math. Sci. (Cambridge, UK), ISF (Israel Scie. Found.), Research Grants Council of Hong Kong, and Binational Science Foundation USA-Israel

Departmental Service

• Chair of the Outreach Committee, 2008 - present.
• Member of the Sub-Committee P, 2008 - present.
• Chair of the Talent Search Committee, 2005 - 2008.
• Member of the Graduate Committee, 2004 - 2006.
• Mentoring four postdocs: E. Chappa (2002-2005), J. Harrison, B. Winn 2004-2005 (the last two jointly with G. Berkolaiko and S. Fulling), A. Skripka (2007 - present)
• Co-organizer (with G. Berkolaiko and S. Fulling) of the special 2004-2005 year on mathematical physics and spectral theory.
• Member of the Endowed Professorhsip Committee, 2004 - present.
• Chair of the Math Awareness Committee (2004-2008). Organized the Math Awareness Open House event, April 2004, 2005, 2006.
• Co-organizer of Math Physics and Harmonic Analysis Seminar.
• Member of the Executive Committee, 2002 - 2004.
• Member of the Postdoc hiring committee 2001 - 2005.

Hobbies

Books, music, travel.

Citizenship

Citizen of the USA

Link to publications (books, papers, and lecture notes for students)

Books in preparation:

• Periodic Partial Differential Equeations and their Applications

• (with M. Agranovsky and E. T. Quinto) Spherical Mean Operators and their Applications

• (with G. Berkolaiko) An Introduction to Quantum Graphs

Conferences organized

• Member of the organizing Committee (with G. Uhlmann (U. Wash.), M. V. van de Hoop(Purdue Univ.), C. Koenig (U. Chicago), L. Paivarinta (Univ. Oulu), M. Zworski (Berkeley), L. Borcea (Rice)) "Inverse problems" semester program, MSRI, Berkeley, August 16 to December 17, 2010.

• Co-organizer (with M. Brown (U. Cardiff), P. Exner (Dopler Inst., Prague), and T. Sunada (Meiji Univ., Tokyo)) of the workshop "Analysis on Graphs", Vambridge Univ., July 2010.

• Chair of the organizing Committee (with D. Finch (Oregon St.), J. Schotland (UPenn), Y. Xu (Ryerson Univ., Canada)), "Mathematical Methods in Novel Modalities of Medical Imaging", Banff, Canada, October 2009.

• Co-organizer (with G. Berkolaiko (Texas A&M), J. Harrison, and K. Kirsten (Baylor Univ.)) of the section "Analysis on Graphs and Singular Manifolds" at the Amer. Math. Soc. Meerting, Baylor Univ., October 2009.

• Co-organizer (with N. Datta (U. Cambridge)) of the section "Non-relativistic quantum mechanics and quantum computation" at the Congress of the Internat. Soc. of Math. Physics, Prague, August 2009.

• Member of the organizing Committee (with M. Braverman (Northeastern), L. Friedlander (U. Arizona), T. Kappeler (Lousanne), J. Weitsman (Northeastern)), "Spectral theory and geometric analysis", Northeastern Univ., Boston, July 2009.

• Organizer, Mini-symposium on "Novel methods of medical imaging" at the Soc. Ind. and Appl. Math. Life Sciences conference, Montreal, August 2008.

• Co-organizer, AMS Special Session on Radon Transform and Tomography, January 2007, New Orleans, LA.

• Member of the Organizing Committee of the 6 month program "Analysis on Graphs and its Applications" at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 8 January - 29 June 2007 (organizational work started in 2004).

• Chair of the Organizing Committee of the Joint Summer Research Conference in the Mathematical Sciences "Quantum Graphs and Their Applications", Snowbird, UT, June 18 -- June 24, 2005.

• Co-organizer of the Joint Summer Research Conference in the Mathematical Sciences "Mathematical Modeling of Novel Optical Devices", Snowbird, UT, June 11 -- June 18, 2005.

• Organizer of the special 2004-2005 year on spectral theory and mathematical physics at Texas A&M.

• Organizer of a mini-workshop on Mathematical Analysis of Photonic Devices, Texas A&M Univ., May 2003.

• Co-Organizer of the Special Session on Inverse problems and Tomography at the AMS Meeting, Binghamton, NY, October 2003.

• Organizer of the Section on Spectral Theory and Wave Propagation at the 2002 UAB International Conference on Differential Equations and Mathematical Physics, Birmingham, Alabama, March 26-30, 2002.

• Organizer of the Joint Summer Research Conference on Waves in Periodic and Random Media, South Hadley, MA, 2002.

• Organizer of the 11th Midwest Geometry Conference, April 2001.

• Co-organizer of the Joint Summer Research Conference on Integral Geometry, Tomography, and Impedance Imaging, South Hadley, MA, June 1993.

Selected Professional Speeches and Presentations

In the past several years numerous invited and contributed talks were presented at international and national meetings and at universities in Australia, Austria, Canada, Chile, China, Czech Republic, France, Germany, Israel, Italy, Japan, South Korea, Sweden, Turkey, UK, and USA. Among the recent ones:

1. Invited Lecture "On reconstructions in thermoacoustic tomography" at the international conference on Integral Geometry and Tomography, Stockholm University, Sweden, August 12-15, 2008

2. Invited Lecture "Mathematical problems of thermoacoustic tomography" at the international conference Inverse Problems: Modeling and Simulation, Oludeniz-Fethiye, Mugla, Turkey, May 26 - 30, 2008.

3. Invited Applied Math Colloquium "Can one hear the heat of a body? Mathematics of thermoacoustic tomography", MIT, Cambridge, MA, April 2008

4. Invited Colloquium "Can one hear the heat of a body? Mathematics of thermoacoustic tomography", Tufts University, Medford, MA, April 2008

5. Invited Lecture "Mathematical problems of thermoacoustic tomography. " at the Special Session on Radon Transforms, Tomography, and Related Geometric Analysis, Amer. Math. Soc. meeting, Louisiana State University, Baton Rouge, LA, 28 - 30 March 2008.

6. Invited Lecture "Mathematical problems of thermoacoustic tomography" at the international "Biomedical imaging" workshop, Radon Inst., Linz, Austria, November 2007.

7. Invited Lecture "Liouville theorems for periodic equations on abelian coverings" at the international conference "Spectral Analysis in Geometry and Number Theory", Nagoya, Japan, August 2007.

8. Invited Lecture "Low dimensional models for wave propagation in thin structures" at the international school "Complex optics in mesoscopic materials", Erice, Sicily, Italy, July 2007.

9. Invited Lecture "Analysis on graphs and its applications", Correspondents Meeting, Isaac Institute for Math. Sciences, Cambridge, UK, June 2007.

10. Invited Lecture "On Representations of Solutions of Periodic Elliptic Equations on Abelian Coverings" at the international conference "Partial Differential Equations and Spectral Theory" dedicated to the 85th birthday of S. Agmon, Hebrew Univ., Jerusalem, Israel, Jan. 28 - Feb. 2, 2007.

11. Series of four invited lectures "Introduction to quantum graphs", workshop "Analysis on graphs and its applications" by the Newton Institute and London Math. Soc., Gregynog, Wales, UK, January 2007.

12. Invited lecture at the Autumn School on Analysis, Simulation and Design of nanotechnological processes, Department of Mathematics, University of Karlsruhe, Karlsruhe, Germany, 17 - 20 October 2006.

13. Keynote lecture at the Opening Ceremony of the Graduate School on Analysis, Simulation and Design of nanotechnological processes, Univ. Karlsruhe, Germany, 17 - 20 October 2006.

14. Invited lecture at the international workshop Inverse Problems and Applications, Banff International Research Station, August 19 - August 24, 2006.

15. Invited lecture at the international workshop Mathematical Methods in Tomography, Mathematisches Forschungsinstitut Oberwolfach, July 30 - August 5, 2006.

16. Invited lecture at the program Spectral Theory and Partial Differential Equations, Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 17 July - 11 August 2006.

17. Invited lecture at the International Conference on Analysis and Applications, University of Science and Technology of China and City University of Hong Kong, Hefei, China, June 28 - 30, 2006.

18. Invited mini-symposium talk at SIAM Conference on Imaging Science, IMA, May 15-17, 2006

19. A course of 6 lectures at the Mathematics Department, Seoul National University, March 2006.

20. Invited lecture at New Mathematics and Algorithms for 3-D Image Analysis, IMA, January 9-12, 2006

21. Plenary talk at 2005 New Zealand Mathematics Colloquium, Massey University, Palmerston North, New Zealand, December 5 - 7, 2005.

22. Invited lecture at 2005 Special Session on New Directions in Spectral Theory and Geometric Analysis, AMS Meeting, Eugene, OR, November 12-13, 2005.

23. Invited lecture at Geometric and Probabilistic Methods in Group Theory and Dynamical Systems,Texas A&M,3 - 6 November 2005

24. Plenary lecture at Multi-scale problems: modelling, analysis and applications, University of Bath, 12th - 14th September 2005

25. Invited seminar talk "Circular Radon transform, theormoacoustic tomography, and all that" at University of Bath 17th September 2005.

26. Invited lecture at the international workshop Geometrical Aspects of Spectral Theory Matrei, East Tirol, Austria July 1-12, 2005.

27. Invited lecture at MolchanovFest, Probability and Mathematical Physics, A Conference in Honor of Stanislav Molchanov's 65th Birthday, Centre de Recherches Mathematiques, Montreal June 27- July 1, 2005.

28. Invited lecture at the AMS Short Course on Radon Transform and its Applications to Inverse Problems, Atlanta, GA, January 2005.

29. Invited lecture at the NanoPhysics section of the international conference QMath9 (Mathematical results of Quantum mechanics), September 2004, Giens, France.

30. Series of 6 invited lectures at the Inverse Problems special year, Univ. Helsinki, May 2004.

31. Invited lecture at the international conference Inverse Problems: Results and Perspectives, Univ. Helsinki, May 2004.

32. Invited talk at the Annual Meeting of the Israel Math. Union, May 2004.

33. Invited lecture at the Inverse Problems workshop at IPAM, November 2003.

34. Plenary address at the 24th Annual Southeastern-Atlantic Regional Conference on Differential Equations, Univ. of Tennessee at Chattanooga, October 22 - 23, 2004.

35. Plenary address at the AMS Meeting in Binghampton, NY, October 2003.

36. Invited mini-course at the Pan-American Advanced Studies Institute (PASI) on Partial Differential Equations, Inverse Problems and Non-Linear Analysis, January 6-18, 2003, Universidad de Chile, Santiago, Chile.

37. Invited lecture at the Mittag-Leffler Institute, Stockholm, Sweden, November 2002.

38. Invited talk at the PECS-IV: International Workshop on Photonic and Electromagnetic Crystal Structures (Jointly Sponsored By PECS-IV and IPAM), UCLA, Los Angeles, CA, October 28-31, 2002.

39. Invited lecture at the International Workshop Guided Quantum Particles: from Mathematics to Mesoscopics, Nuclear Physics Institute, Academy of Sciences, and Doppler Institute for Mathematical Physics, Prague, Czech Republic, June 9-15, 2002.

40. Plenary address at the 3rd International Congress of ISAAC (Internat. Soc. Anal. Appl. Comp), Berlin, August 2001.

Educational activities

• Organizer (1994-1995) and teacher (1994-2001) of the Math Club for middle school students.

• Organizer (1994) and the Head of the Committee (1994 - 2001) of the Kansas Outreach School in Mathematics (KOSM), a program for middle and high school students.

• Author of several booklets for KOSM students (see publications)

• Teaching at the Summer Educational Enrichment in Math program for middle school students, TAMU, 2002-2005, 2008.

• Chair of the Math Awareness Committee (Texas A&M) 2003-2008.

• Chair of the Talent Search Committee (Texas A&M) 2005 - 2008.

• Chair of the Outreach Committee (Texas A&M) 2008 - present.

• Judge, SIAM student paper contest, 2008.

• Member, MAA Math Circles group, 2008-present.

• Organizer (2008-present) of the High School Math Summer Camp at Texas A&M.