HR job title
- Distinguished Professor
- Contact Info
- Websites
- ORCiD
- 0000-0001-8789-5246
Kuchment, Peter Distinguished Professor
Positions
- Distinguished Professor, Mathematics, College of Arts and Sciences
Major research articles, books, surveys, and presentations around the world on inverse problems (with applications to medical and homeland security imaging), material science (photonic crystals, nanostructures), spectral theory 9with math physics applications), and quantum graphs.
Research Areas
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- Research
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- Works By Students
- Background
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Overview
Publications
selected publications
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academic article
-
Kuchment, P.
(2023).
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown. Journal of Mathematical Physics.
64(11), 113504.
-
Berkolaiko, G., & Kuchment, P.
(2022).
Spectral shift via "lateral" perturbation. Journal of Spectral Theory.
12(1), 83-104.
-
Kuchment, P., & Taskinen, J.
(2022).
Dispersion relations and spectra of periodically perforated structures. Pure and Applied Functional Analysis.
7(2), 721-731.
-
Kha, M., & Kuchment, P.
(2021).
Liouville-Riemann-Roch Theorems on Abelian Coverings. Lecture Notes in Mathematics.
2245, 1-93.
-
Kuchment, P.
(2021).
Three-Representation Problem in Banach Spaces. Complex Analysis and Operator Theory.
15(2), 34.
-
Kuchment, P.
(2021).
Three-representation problem. Complex Analysis and Operator Theory.
15(2),
-
Braverman, M., Dikansky, A., Friedlander, L., Gromov, M., Ivrii, V., Kordyukov, Y., ... Zvonkin, A.
(2021).
Mikhail Aleksandrovich Shubin (19442020). Notices of the American Mathematical Society.
68(01), 1-1.
-
Braverman, M., Buchstaber, V. M., Gromov, M., Ivrii, V., Kordyukov, Y. A., Kuchment, P., ... Khovanskii, A. G.
(2020).
obituary Mikhail Aleksandrovich Shubin. 75(6), 1143-1152.
-
Berkolaiko, G., & Kuchment, P.
(2020).
Spectral shift via "lateral" perturbation. 12(1), 83-104.
-
Braverman, M., Buchstaber, V. M., Gromov, M. L., Ivrii, V. Y., Kordyukov, Y. A., Kuchment, P. A., ... Khovanskii, A. G.
(2020).
Mikhail Aleksandrovich Shubin (obituary). Russian Mathematical Surveys.
75(6(456)), 162-170.
-
Ngoc, D. o., Kuchment, P., & Sottile, F.
(2020).
Generic properties of dispersion relations for discrete periodic operators. Journal of Mathematical Physics.
61(10), 103502-103502.
-
Baines, W., Kuchment, P., & Ragusa, J.
(2020).
Deep learning for 2D passive source detection in presence of complex cargo. Inverse Problems.
36(10), 104001-104001.
-
Agranovsky, M., Baras, J., Chang, D., Gay, R., Li, B. Q., Kuchment, P., ... Yger, A.
(2020).
Remembering Carlos A. Berenstein (19442019). Notices of the American Mathematical Society.
67(08), 1-1.
-
Braverman, M., Dikansky, A., Friedlander, L., Gromov, M., Ivrii, V., Kordyukov, Y., ... Zvonkin, A.
(2020).
Mikhail Aleksandrovich Shubin. December 19, 1944 -- May 13, 2020
-
Braverman, M., Buchshtaber, B. M., Gromov, M., Ivrii, V., Kordyukov, Y. A., Kuchment, P., ... Khovanskii, A. G.
(2020).
Misha Shubin. 1944 -- 2020
-
Kuchment, P., & Zhao, J.
(2019).
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs. Journal of Mathematical Physics.
60(9), 093502-093502.
-
Corbin, J. E., & Kuchment, P.
(2019).
Spectra of "fattened" open book structures
-
Egorov, Y. V., Komech, A. I., Kuchment, P. A., Lakshtanov, E. L., Maz'ya, V. G., Molchanov, S. A., Novikov, R. G., & Freidlin, M. I.
(2019).
Boris Rufimovich Vainberg (on his 80th birthday). Russian Mathematical Surveys.
74(1), 181-186.
-
, ., Egorov, Y. V., , ., Komech, A. I., , ., Kuchment, P. A., ... Freidlin, M. I.
(2019).
Boris Rufimovich Vainberg (on his 80th birthday). Russian Mathematical Surveys.
74(1(445)), 189-194.
-
Kuchment, P., & Lvin, S.
(2019).
Some binomial formulas for non-commuting operators. 733, 197-207.
-
Egorov, Y., Komech, A., Kuchment, P., Lakshtanov, E., Mazya, V., Molchanov, S., Novikov, R., & Freidlin, M.
(2018).
Boris R. Vainberg (on his 80th birthday)
-
Terzioglu, F., Kuchment, P., & Kunyansky, L.
(2018).
Compton camera imaging and the cone transform: a brief overview. Inverse Problems.
34(5), 054002-054002.
-
Buchstaber, V. M., Kuchment, P. A., Novikov, S. P., & Semenov, E. M.
(2018).
To the memory of Selim Grigor'evich Krein (1917-1998). Russian Mathematical Surveys.
73(1), 187-190.
-
Auckly, D., & Kuchment, P.
(2018).
On Parseval frames of exponentially decaying composite Wannier functions. Contemporary Mathematics.
717, 227-240.
-
, ., Buchstaber, V. M., , ., Kuchment, P. A., , ., Novikov, S. P., e, ., & Semenov, E. M.
(2018).
To the memory of Selim Grigor'evich Krein (1917 - 1998). Russian Mathematical Surveys.
73(1(439)), 191-193.
-
Kuchment, P., & Terzioglu, F.
(2017).
INVERSION OF WEIGHTED DIVERGENT BEAM AND CONE TRANSFORMS. Inverse Problems and Imaging.
11(6), 1071-1090.
-
Kha, M., Kuchment, P., & Raich, A.
(2017).
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior. Journal of Spectral Theory.
7(4), 1171-1233.
-
Agranovsky, M., Kuchment, P., & Kunyansky, L.
(2017).
On reconstruction formulas and algorithms for the thermoacoustic tomography. 89-101.
-
Olson, A., Ciabatti, A., Hristova, Y., Kuchment, P., Ragusa, J., & Allmarasd, M.
(2016).
Passive Detection of Small Low-Emission Sources: Two-Dimensional Numerical Case Studies. Nuclear Science and Engineering.
184(1), 125-150.
-
Kuchment, P., & Terzioglu, F.
(2016).
3D Image Reconstruction from Compton camera data
-
Kuchment, P.
(2016).
AN OVERVIEW OF PERIODIC ELLIPTIC OPERATORS. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
53(3), 343-414.
-
Kuchment, P.
(2016).
On a problem concerning affine-invariant points of convex sets
-
Do, N. T., Kuchment, P., & Ong, B.
(2016).
On resonant spectral gap opening in quantum graph networks
-
Kuchment, P., & Terzioglu, F.
(2016).
Three-Dimensional Image Reconstruction from Compton Camera Data. 9(4), 1708-1725.
-
Kuchment, P., & Steinhauer, D.
(2015).
Stabilizing inverse problems by internal data. II: non-local internal data and generic linearized uniqueness. 5(4), 391-425.
-
Kuchment, P.
(2015).
Book Review: Climate modeling for scientists and engineers. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY.
52(3), 519-520.
-
Kuchment, P., & Kunyansky, L.
(2015).
Mathematics of Photoacoustic and Thermoacoustic Tomography. 1117-1167.
-
Olson, A., Ciabatti, A., Hristova, Y., Kuchment, P., Ragusa, J., Charlton, W., & Allmaras, M.
(2013).
Detection of small low emission sources - case studies
-
Kuchment, P., & Lvin, S.
(2013).
Identities for sin x that Came from Medical Imaging. 120(7), 609-621.
-
Allmaras, M., Darrow, D., Hristova, Y., Kanschat, G., & Kuchment, P.
(2013).
DETECTING SMALL LOW EMISSION RADIATING SOURCES. 7(1), 47-79.
-
T., N., & Kuchment, P.
(2013).
Quantum graph spectra of a graphyne structure. Nanoscale Systems: Mathematical Modeling, Theory and Applications.
2(1), 107-123.
-
Berkolaiko, G., Kuchment, P., & Smilansky, U.
(2012).
CRITICAL PARTITIONS AND NODAL DEFICIENCY OF BILLIARD EIGENFUNCTIONS. GEOMETRIC AND FUNCTIONAL ANALYSIS.
22(6), 1517-1540.
-
Kuchment, P., & Raich, A.
(2012).
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case. Mathematische Nachrichten.
285(14-15), 1880-1894.
-
Berkolaiko, G., & Kuchment, P.
(2012).
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. 84, 117-137.
-
Howson, W. P., & Watson, A.
(2012).
Homogeneous trees of second order SturmLiouville equations: A general theory and program. Computers and Structures.
104, 13-20.
-
Kuchment, P., & Steinhauer, D.
(2012).
Stabilizing inverse problems by internal data. 28(8), 084007-084007.
-
Kuchment, P.
(2012).
Leon Ehrenpreis, Recollections from the Recent Decades. Springer Proceedings in Mathematics.
16, 15-21.
-
Kuchment, P.
(2012).
Mathematics of Hybrid Imaging: A Brief Review. Springer Proceedings in Mathematics.
16, 183-208.
-
Allmaras, M., & Bangerth, W.
(2011).
Reconstructions in ultrasound modulated optical tomography. Journal of Inverse and Ill-posed Problems.
19(6), 801-823.
-
Xun, X., Mallick, B., Carroll, R. J., & Kuchment, P.
(2011).
A Bayesian approach to the detection of small low emission sources. Inverse Problems.
27(11), 115009-115009.
-
Kuchment, P., & Raich, A.
(2011).
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
-
Kuchment, P., & Kunyansky, L.
(2011).
2D and 3D reconstructions in acousto-electric tomography. Inverse Problems.
27(5), 055013-055013.
-
Agranovsky, M., & Kuchment, P.
(2011).
THE SUPPORT THEOREM FOR THE SINGLE RADIUS SPHERICAL MEAN TRANSFORM. Memoirs on Differential Equations and Mathematical Physics.
52, 1-16.
-
Agranovsky, M., & Kuchment, P.
(2011).
The support theorem for the single radius spherical mean transform. Memoirs on Differential Equations and Mathematical Physics.
52, 1-16.
-
Exner, P., Kuchment, P., & Winn, B.
(2010).
On the location of spectral edges in Z-periodic media. Journal of Physics A: Mathematical and Theoretical.
43(47), 474022-474022.
-
Kuchment, P., & Kunyansky, L.
(2010).
SYNTHETIC FOCUSING IN ULTRASOUND MODULATED TOMOGRAPHY. 4(4), 665-673.
-
Kuchment, P., & Ong, B.
(2009).
On guided electromagnetic waves in photonic crystal waveguides
-
Agranovsky, M., Finch, D., & Kuchment, P.
(2009).
RANGE CONDITIONS FOR A SPHERICAL MEAN TRANSFORM. Inverse Problems and Imaging.
3(3), 373-382.
-
Kuchment, P.
(2009).
Tight frames of exponentially decaying Wannier functions. Journal of Physics A: Mathematical and Theoretical.
42(2), 025203-025203.
-
Hristova, Y., Kuchment, P., & Nguyen, L.
(2008).
Reconstruction and time reversal in thermoacoustic tomography in acoustically homogeneous and inhomogeneous media. 24(5), 055006-055006.
-
Kuchment, P., & Kunyansky, L.
(2008).
A survey in mathematics for industry mathematics of thermoacoustic tomography. 19(2), 191-224.
-
Kuchment, P., & Pinchover, Y.
(2007).
Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds. Transactions of the American Mathematical Society.
359(12), 5777-5815.
-
Kuchment, P., & Post, O.
(2007).
On the spectra of carbon nano-structures. Communications in Mathematical Physics.
275(3), 805-826.
-
Fulling, S. A., Kuchment, P., & Wilson, J. H.
(2007).
Index theorems for quantum graphs. Journal of Physics A: Mathematical and Theoretical.
40(47), 14165-14180.
-
Agranovsky, M., & Kuchment, P.
(2007).
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography with variable sound speed. Inverse Problems.
23(5), 2089-2102.
-
Harrison, J. M., Kuchment, P., Sobolev, A., & Winn, B.
(2007).
On occurrence of spectral edges for periodic operators inside the Brillouin zone. Journal of Physics A: Mathematical and Theoretical.
40(27), 7597-7618.
-
Agranovsky, M., Kuchment, P., & Quinto, E. T.
(2007).
Range descriptions for the spherical mean Radon transform. Journal of Functional Analysis.
248(2), 344-386.
-
Kuchment, P., & Kunyansky, L.
(2007).
Mathematics of thermoacoustic tomography
-
Kuchment, P.
(2007).
Integral representations of solutions of periodic elliptic equations. 42, 323-339.
-
Kuchment, P., & Vainberg, B.
(2006).
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators. Communications in Mathematical Physics.
268(3), 673-686.
-
Ambartsoumian, G., & Kuchment, P.
(2006).
A range description for the planar circular radon transform. SIAM Journal on Mathematical Analysis.
38(2), 681-692.
-
Fulling, S. A., & Kuchment, P.
(2005).
Coincidence of length spectra does not imply isospectrality. Inverse Problems.
21(4), 1391-1395.
-
Kuchment, P.
(2005).
Quantum graphs: II. Some spectral properties of quantum and combinatorial graphs. Journal of Physics A: Mathematical and General.
38(22), 4887-4900.
-
Ambartsoumian, G., & Kuchment, P.
(2005).
On the injectivity of the circular Radon transform. Inverse Problems.
21(2), 473-485.
-
Xu, Y., Wang, L. V., Ambartsoumian, G., & Kuchment, P.
(2004).
Reconstructions in limited-view thermoacoustic tomography. Medical Physics.
31(4), 724-733.
-
Kuchment, P.
(2004).
Quantum graphs. Waves in Random and Complex Media.
14(1), S3-S5.
-
Kuchment, P.
(2004).
Quantum graphs: I. Some basic structures. Waves in Random and Complex Media.
14(1), S107-S128.
-
Kuchment, P.
(2002).
Call for papers for a special issue on Quantum Graphs and their Applications. Waves in Random and Complex Media.
12(4), e3-e3.
-
Kuchment, P.
(2002).
Graph models for waves in thin structures. Waves in Random and Complex Media.
12(4), R1-R24.
-
Kuchment, P., & Levendorskii, S.
(2002).
On the structure of spectra of periodic elliptic operators. 354(2), 537-569.
-
Kuchment, P., & Kunyansky, L.
(2002).
Differential operators on graphs and photonic crystals. Advances in Computational Mathematics.
16(2-3), 263-290.
-
Kuchment, P., & Zeng, H. B.
(2001).
Convergence of spectra of mesoscopic systems collapsing onto a graph. Journal of Mathematical Analysis and Applications.
258(2), 671-700.
-
Kuchment, P.
(2001).
Integral representations and Liouville theorems for solutions of periodic elliptic equations. Journal of Functional Analysis.
181(2), 402-446.
-
Fridman, B., Kuchment, P., Lancaster, K., Lissianoi, S., Mogilevsky, M., Ma, D., Ponomarev, I., & Papanicolaou, V.
(2000).
Numerical harmonic analysis on the hyperbolic plane. Applicable Analysis: an international journal.
76(3-4), 351-362.
-
Kuchment, P., & Vainberg, B.
(2000).
On absence of embedded eigenvalues for Schrodinger operators with perturbed periodic potentials. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS.
25(9-10), 1809-1826.
-
, ., Brezanskii, Y. M., , ., Gindikin, S. G., , ., Kutateladze, S. S., ... Tikhomirov, V. M.
(2000).
Selim Grigor'evich Krein (obituary). Russian Mathematical Surveys.
55(2), 125-126.
-
Kuchment, P., & Levendorskii, S.
(1999).
On absolute continuity of spectra of periodic elliptic operators. Operator Theory Advances and Applications.
108, 291-297.
-
Axmann, W., & Kuchment, P.
(1999).
An efficient finite element method for computing spectra of photonic and acoustic band-gap materials - I. Scalar case. Journal of Computational Physics.
150(2), 468-481.
-
Kuchment, P.
(1999).
DEPSCoR Project Mathematical Analysis of Photonic Band-Gap Materials 1997-2000
-
Axmann, W., Kuchment, P., & Kunyansky, L.
(1999).
Asymptotic methods for thin high-contrast two-dimensional PBG materials. Journal of Lightwave Technology.
17(11), 1996-2007.
-
Kuchment, P., & Kunyansky, L. A.
(1999).
Spectral properties of high contrast band-gap materials and operators on graphs. Experimental Mathematics.
8(1), 1-28.
-
Figotin, A., & Kuchment, P.
(1998).
Spectral properties of classical waves in high-contrast periodic media. 58(2), 683-702.
-
Figotin, A., & Kuchment, P.
(1996).
Band-gap structure of spectra of periodic dielectric and acoustic media .2. Two-dimensional photonic crystals. 56(6), 1561-1620.
-
Aguilar, V., Ehrenpreis, L., & Kuchment, P.
(1996).
Range conditions for the exponential radon transform. 68(1), 1-13.
-
Agranovsky, M., Berenstein, C., & Kuchment, P.
(1996).
Approximation by spherical waves inLp-spaces. Journal of Geometric Analysis.
6(3), 365-383.
-
Figotin, A., & Kuchment, P.
(1996).
Band-gap structure of spectra of periodic dielectric and acoustic media .1. Scalar model. SIAM Journal on Applied Mathematics.
56(1), 68-88.
-
AGUILAR, V., & KUCHMENT, P.
(1995).
RANGE CONDITIONS FOR THE MULTIDIMENSIONAL EXPONENTIAL X-RAY TRANSFORM. Inverse Problems.
11(5), 977-982.
-
KUCHMENT, P., LANCASTER, K., & MOGILEVSKAYA, L.
(1995).
ON LOCAL TOMOGRAPHY. Inverse Problems.
11(3), 571-589.
-
Shneiberg, L.
(1994).
Some inversion formulas in the single photon emission computed tomography. Applicable Analysis: an international journal.
53(3-4), 221-231.
-
KUCHMENT, P.
(1994).
ON THE BEHAVIOR OF FLOQUET EXPONENTS OF A KIND OF PERIODIC EVOLUTION PROBLEMS. Journal of Differential Equations.
109(2), 309-324.
-
FIGOTIN, A., & KUCHMENT, P.
(1994).
BAND-GAP STRUCTURE OF THE SPECTRUM OF PERIODIC MAXWELL OPERATORS. 74(1-2), 447-455.
-
Kuchment, P. A., & L'Vin, S. Y.
(1990).
Paley-Wiener theorem for exponential Radon transform. Acta Applicandae Mathematicae.
18(3), 251-260.
-
Kuchment, P. A.
(1988).
Singularities of the boundary of the stability region in the infinite-dimensional case. Functional Analysis and Its Applications.
22(3), 232-233.
-
Berezanskii, Y. M., Bogolyubov, N. N., Kuchment, P. A., Levin, B. Y., Maslov, V. P., Novikov, S. P., & Semnov, E. M.
(1987).
Selim Grigor'evich Krein (on his seventieth birthday). Russian Mathematical Surveys.
42(5), 181-183.
-
Kuchment, P. A.
(1986).
SPHERICAL REPRESENTATION OF SOLUTIONS OF INVARIANT DIFFERENTIAL EQUATIONS ON A RIEMANNIAN SYMMETRIC SPACE OF NONCOMPACT TYPE. Mathematics of the USSR - Izvestija.
27(3), 535-548.
-
Kuchment, P. A.
(1983).
REPRESENTATIONS OF SOLUTIONS OF PERIODIC PARTIAL DIFFERENTIAL EQUATIONS. Mathematics of the USSR - Izvestija.
21(1), 93-117.
-
Kuchment, P. A.
(1982).
Floquet theory for partial differential equations. Russian Mathematical Surveys.
37(4), 1-60.
-
Kuchment, P. A.
(1982).
Functions on symmetric spaces which are periodic in the mean. Functional Analysis and Its Applications.
16(3), 213-214.
-
Kuchment, P. A.
(1980).
THE ABSENCE OF L2-SOLUTIONS FOR PERIODIC PARTIAL DIFFERENTIAL EQUATIONS. Russian Mathematical Surveys.
35(2), 247-248.
-
Kuchment, P. A.
(1980).
Bloch solutions of periodic partial differential equations. Functional Analysis and Its Applications.
14(1), 52-53.
-
Kuchment, P. A.
(1979).
ON THE FLOQUET THEORY FOR PERIODIC LINEAR DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENT. Russian Mathematical Surveys.
34(3), 205-206.
-
Kuchment, P. A.
(1979).
Floquet representation of solutions of linear hypoelliptic systems of partial differential equations. Functional Analysis and Its Applications.
13(1), 59-60.
-
Kuchment, P. A.
(1976).
Reconstruction of a continuous representation with respect to a subrepresentation and a factor representation. Functional Analysis and Its Applications.
10(1), 67-68.
-
Zaidenberg, M. G., Krein, S. G., Kuchment, P. A., & Pankov, A. A.
(1975).
BANACH BUNDLES AND LINEAR OPERATORS. Russian Mathematical Surveys.
30(5), 115-175.
-
Krasnenker, A. S., & Kuchment, P. A.
(1972).
Some sufficient conditions for the existence of nonhomogeneous flows in networks. Cybernetics and Systems Analysis.
8(4), 685-688.
-
Kuchment, P.
(2023).
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown. Journal of Mathematical Physics.
64(11), 113504.
-
book
-
Kuchment, P.
(2014).
Radon Transform and Medical Imaging. Ed. 85.
Society for Industrial & Applied Mathematics (SIAM).
-
Berkolaiko, G., & Kuchment, P.
(2013).
Introduction to Quantum Graphs. American Mathematical Soc..
-
Berkolaiko, G., & Kuchment, P.
(2012).
Introduction to Quantum Graphs. Ed. 186.
American Mathematical Society (AMS).
-
Kuchment, P.
(1993).
Floquet Theory for Partial Differential Equations. Springer Nature.
-
Kuchment, P.
(2014).
Radon Transform and Medical Imaging. Ed. 85.
Society for Industrial & Applied Mathematics (SIAM).
-
chapter
-
Kha, M., & Kuchment, P.
(2021).
Auxiliary Statements and Proofs of Technical Lemmas. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 67-84).
Springer International Publishing.
-
Kha, M., & Kuchment, P.
(2021).
Final Remarks and Conclusions. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 85-86).
-
Kha, M., & Kuchment, P.
(2021).
Liouville-Riemann-Roch Theorems on Abelian Coverings Preface. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. VII-+).
-
Kha, M., & Kuchment, P.
(2021).
Preliminaries. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 1-21).
Springer International Publishing.
-
Kha, M., & Kuchment, P.
(2021).
Proofs of the Main Results. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 35-53).
Springer International Publishing.
-
Kha, M., & Kuchment, P.
(2021).
Specific Examples of Liouville-Riemann-Roch Theorems. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 55-66).
Springer International Publishing.
-
Kha, M., & Kuchment, P.
(2021).
The Main Results. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 23-33).
Springer International Publishing.
-
Corbin, J. E., & Kuchment, P.
(2020).
Spectra of fattened open book structures. Aron, R. M., Gallardo Gutiérrez, E. A., Martin, M., Ryabogin, D., Spitkovsky, I. M., & Zvavitch, A. (Eds.),
Operator Theory.
(pp. 99-108).
DE GRUYTER.
-
Kuchment, P., & Semenov, E.
(2019).
CONTEMPORARY MATHEMATICS Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial Introduction. Contemporary Mathematics.
DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, AND APPLICATIONS: SELIM GRIGORIEVICH KREIN CENTENNIAL.
(pp. 1-15).
-
Kuchment, P., & Semenov, E.
(2019).
CONTEMPORARY MATHEMATICS Differential Equations, Mathematical Physics, and Applications: Selim Grigorievich Krein Centennial Preface. Contemporary Mathematics.
DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, AND APPLICATIONS: SELIM GRIGORIEVICH KREIN CENTENNIAL.
(pp. IX-IX).
-
Kuchment, P., & Semenov, E.
(2019).
Functional Analysis and Geometry: Selim Grigorievich Krein Centennial Introduction. Contemporary Mathematics.
FUNCTIONAL ANALYSIS AND GEOMETRY: SELIM GRIGORIEVICH KREIN CENTENNIAL.
(pp. 1-15).
-
Kuchment, P., & Semenov, E.
(2019).
Functional Analysis and Geometry: Selim Grigorievich Krein Centennial Preface. Contemporary Mathematics.
FUNCTIONAL ANALYSIS AND GEOMETRY: SELIM GRIGORIEVICH KREIN CENTENNIAL.
(pp. XI-XI).
-
Kuchment, P., & Lvin, S.
(2019).
Some binomial formulas for non-commuting operators. Contemporary Mathematics.
FUNCTIONAL ANALYSIS AND GEOMETRY: SELIM GRIGORIEVICH KREIN CENTENNIAL.
(pp. 197-207).
-
Kuchment, P., & Semenov, E.
(2019).
Introduction. Functional Analysis and Geometry.
(pp. 1-15).
American Mathematical Society (AMS).
-
Kuchment, P., & Semenov, E.
(2019).
Introduction. Differential Equations, Mathematical Physics, and Applications.
(pp. 1-15).
American Mathematical Society (AMS).
-
Kuchment, P., & Lin, V.
(2019).
Selim Krein and Voronezh Winter Mathematical Schools. Contemporary Mathematics.
DIFFERENTIAL EQUATIONS, MATHEMATICAL PHYSICS, AND APPLICATIONS: SELIM GRIGORIEVICH KREIN CENTENNIAL.
(pp. 29-34).
American Mathematical Society (AMS).
-
Do, N. T., Kuchment, P., & Ong, B.
(2017).
On resonant spectral gaps in quantum graphs. FUNCTIONAL ANALYSIS AND OPERATOR THEORY FOR QUANTUM PHYSICS: THE PAVEL EXNER ANNIVERSARY VOLUME.
(pp. 213-222).
European Mathematical Society - EMS - Publishing House GmbH.
-
Xu, Y., Wang, L. V., Ambartsoumian, G., & Kuchment, P.
(2017).
Photoacoustic Imaging and Spectroscopy. Wang, L. V. (Eds.),
Photoacoustic Imaging and Spectroscopy.
(pp. 61-73).
CRC Press.
-
Kuchment, P., & Scherzer, O.
(2015).
Tomography, Photoacoustic, and Thermoacoustic. Encyclopedia of Applied and Computational Mathematics.
(pp. 1488-1496).
Springer Nature.
-
Kuchment, P.
(2014).
"Standard" CT and X-ray and Radon Transforms. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 21-51).
-
Kuchment, P.
(2014).
A Brief Overview of Numerical Methods. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 83-86).
-
Kuchment, P.
(2014).
A Brief and Incomplete History of CT. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 7-9).
-
Kuchment, P.
(2014).
Artifacts, Incomplete Data, Microlocal Analysis, and Such. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 65-75).
-
Kuchment, P.
(2014).
Emission Tomography. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 53-63).
-
Kuchment, P.
(2014).
Inverse Problems with Interior Information. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 151-156).
-
Kuchment, P.
(2014).
MRI, EIT, OT, Elastography, UT. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 87-92).
-
Kuchment, P.
(2014).
More about 3D Radon and X-ray Transforms. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 77-81).
-
Kuchment, P.
(2014).
Organization of the Book. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 15-17).
-
Kuchment, P.
(2014).
Some Major CT Modalities and Their Features to Watch for. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 11-14).
-
Kuchment, P.
(2014).
The Radon Transform and Medical Imaging Preface. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. XV-+).
-
Kuchment, P.
(2014).
Thermo-, Photo-, and Optoacoustic Tomography (TAT/PAT/OAT). RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 97-139).
-
Kuchment, P.
(2014).
Ultrasound Modulation in EIT and OT. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 141-149).
-
Kuchment, P.
(2014).
Why Use Mathematics in Medical Imaging?. RADON TRANSFORM AND MEDICAL IMAGING.
(pp. 3-5).
-
Kuchment, P., & Kunyansky, L.
(2011).
Mathematics of Photoacoustic and Thermoacoustic Tomography. Handbook of Mathematical Methods in Imaging.
(pp. 817-865).
Springer Nature.
-
Xu, Y., Wang, L. V., Ambartsoumian, G., & Kuchment, P.
(2009).
Limited View Thermoacoustic Tomography. PHOTOACCOUSTIC IMAGING AND SPECTROSCOPY.
(pp. 61-73).
Taylor & Francis.
-
Agranovsky, M., Kuchment, P., & Kunyansky, L.
(2009).
On Reconstruction Formulas and Algorithms for the Thermoacoustic Tomography. PHOTOACCOUSTIC IMAGING AND SPECTROSCOPY.
(pp. 89-101).
Taylor & Francis.
-
Xu, Y., Ambartsoumian, G., & Kuchment, P.
(2009).
Limited View Thermoacoustic Tomography. Photoacoustic Imaging and Spectroscopy.
(pp. 64-73).
Taylor & Francis.
-
Agranovsky, M., Kuchment, P., & Kunyansky, L.
(2009).
On Reconstruction Formulas and Algorithms for the Thermoacoustic Tomography. Photoacoustic Imaging and Spectroscopy.
(pp. 89-101).
Taylor & Francis.
-
Kuchment, P.
(2004).
On some spectral problems of mathematical physics. Partial Differential Equations and Inverse Problems.
(pp. 241-276).
American Mathematical Society (AMS).
-
Kuchment, P., & Zeng, H.
(2003).
Asymptotics of spectra of Neumann Laplacians in thin domains. Advances in Differential Equations and Mathematical Physics.
(pp. 199-213).
American Mathematical Society (AMS).
-
Kuchment, P., & Ong, B.
(2003).
On guided waves in photonic crystal waveguides. Waves in Periodic and Random Media.
(pp. 105-115).
American Mathematical Society (AMS).
-
Kuchment, P.
(2001).
7. The Mathematics of Photonic Crystals. Bao, G., Cowsar, L. C., & Masters, W. (Eds.),
Mathematical Modeling in Optical Science.
(pp. 207-272).
Society for Industrial & Applied Mathematics (SIAM).
-
Ehrenpreis, L., Kuchment, P., & Panchenko, A.
(2000).
The exponential X-ray transform and Fritz Johns equation. I. Range description. Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis.
(pp. 173-188).
American Mathematical Society (AMS).
-
Figotin, A., & Kuchment, P.
(1998).
2d photonic crystals with cubic structure: asymptotic analysis. Ima Volumes in Mathematics and Its Applications.
Wave Propagation in Complex Media.
(pp. 23-30).
Springer Nature.
-
Kuchment, P.
(1992).
On positivity problems for the Radon transform and some related transforms. Geometric Analysis.
(pp. 87-95).
American Mathematical Society (AMS).
-
Kuchment, P. A.
(1986).
On the spectral synthesis in the spaces of solutions of invariant differential equations. Lecture Notes in Mathematics.
Global Analysis Studies and Applications II.
(pp. 85-100).
Springer Nature.
-
Kha, M., & Kuchment, P.
(2021).
Auxiliary Statements and Proofs of Technical Lemmas. Lecture Notes in Mathematics.
LIOUVILLE-RIEMANN-ROCH THEOREMS ON ABELIAN COVERINGS.
(pp. 67-84).
Springer International Publishing.
-
conference paper
-
Kuchment, P.
(2020).
Misterio de dominio nodal. 184-191.
-
Kuchment, P.
(2014).
CBMS-NSF Regional Conference Series in Applied Mathematics: Preface
-
Folden, C., Charlton, W. S., Ford, D., Kuchment, P., Rundell, W., & Tribble, R. E.
(2010).
Master's-level certificate program in nuclear forensics at Texas A&M University. ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY.
-
Kuchment, P.
(2008).
Quantum graphs: an introduction and a brief survey. 291-312.
-
Kuchment, P.
(2006).
Generalized transforms of Radon type and their applications. 67-91.
-
Benchama, N., & Kuchment, P.
(2003).
An asymptotic model for wave propagation in thin high contrast 2D acoustic media. 647-650.
-
Kuchment, P.
(2003).
Differential and pseudo-differential operators on graphs as models of mesoscopic systems. ANALYSIS AND APPLICATIONS - ISAAC 2001.
7-30.
-
Kuchment, P., & Vainberg, B.
(1998).
On embedded eigenvalues of perturbed periodic Schrodinger operators. 67-76.
-
KUCHMENT, P.
(1994).
On inversion and range characterization of one transform arising in emission tomography. 240-248.
-
Kuchment, P.
(2020).
Misterio de dominio nodal. 184-191.
-
institutional repository document
-
Kuchment, P.
(2023).
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown
-
Berkolaiko, G., & Kuchment, P.
(2020).
Spectral shift via "lateral" perturbation
-
Braverman, M., Dikansky, A., Friedlander, L., Gromov, M., Ivrii, V., Kordyukov, Y., ... Zvonkin, A.
(2020).
Mikhail Aleksandrovich Shubin. December 19, 1944 -- May 13, 2020
-
Braverman, M., Buchshtaber, B. M., Gromov, M., Ivrii, V., Kordyukov, Y. A., Kuchment, P., ... Khovanskii, A. G.
(2020).
Misha Shubin. 1944 -- 2020
-
Kuchment, P., & Taskinen, J.
(2020).
Dispersion relations and spectra of periodically perforated structures
-
Kuchment, P.
(2020).
Three-representation problem
-
Baines, W., Kuchment, P., & Ragusa, J.
(2020).
Deep learning for 2D passive source detection in presence of complex cargo
-
Do, N. T., Kuchment, P., & Sottile, F.
(2019).
Generic properties of dispersion relations for discrete periodic operators
-
Kha, M., & Kuchment, P.
(2019).
Liouville-Riemann-Roch theorems on abelian coverings
-
Corbin, J. E., & Kuchment, P.
(2019).
Spectra of "fattened" open book structures
-
Kuchment, P., & Zhao, J.
(2019).
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs
-
Egorov, Y., Komech, A., Kuchment, P., Lakshtanov, E., Mazya, V., Molchanov, S., Novikov, R., & Freidlin, M.
(2018).
Boris R. Vainberg (on his 80th birthday)
-
Kuchment, P., & Lvin, S.
(2018).
Some binomial formulas for non-commuting operators
-
Auckly, D., & Kuchment, P.
(2017).
On Parseval frames of exponentially decaying composite Wannier functions
-
Kuchment, P., & Terzioglu, F.
(2016).
Inversion of Weighted Divergent Beam and Cone Transforms
-
Kuchment, P., & Terzioglu, F.
(2016).
3D Image Reconstruction from Compton camera data
-
Kuchment, P.
(2016).
On a problem concerning affine-invariant points of convex sets
-
Do, N. T., Kuchment, P., & Ong, B.
(2016).
On resonant spectral gap opening in quantum graph networks
-
Kuchment, P.
(2015).
An overview of periodic elliptic operators
-
Kha, M., Kuchment, P., & Raich, A.
(2015).
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior
-
Kuchment, P., & Steinhauer, D.
(2014).
Stabilizing inverse problems by internal data. II. Non-local internal data and generic linearized uniqueness
-
Olson, A., Ciabatti, A., Hristova, Y., Kuchment, P., Ragusa, J., Charlton, W., & Allmaras, M.
(2013).
Detection of small low emission sources - case studies
-
Do, N. T., & Kuchment, P.
(2013).
Quantum graph spectra of a graphyne structure
-
Kuchment, P., & Raich, A.
(2011).
Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case
-
Kuchment, P., & Lvin, S.
(2011).
Identities for sin(x) that came from medical imaging
-
Kuchment, P., & Steinhauer, D.
(2011).
Stabilizing Inverse Problems by Internal Data
-
Xun, X., Mallick, B., Carroll, R. J., & Kuchment, P.
(2011).
A Bayesian Approach to Detection of Small Low Emission Sources
-
Berkolaiko, G., Kuchment, P., & Smilansky, U.
(2011).
Critical partitions and nodal deficiency of billiard eigenfunctions
-
Kuchment, P.
(2011).
Mathematics of Hybrid Imaging. A Brief Review
-
Allmaras, M., Darrow, D. P., Hristova, Y., Kanschat, G., & Kuchment, P.
(2010).
Detecting small low emission radiating sources
-
Kuchment, P., & Kunyansky, L.
(2010).
2D and 3D reconstructions in acousto-electric tomography
-
Berkolaiko, G., & Kuchment, P.
(2010).
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths
-
Exner, P., Kuchment, P., & Winn, B.
(2010).
On the location of spectral edges in $mathbb{Z}$-periodic media
-
Kuchment, P., & Kunyansky, L.
(2009).
Mathematics of Photoacoustic and Thermoacoustic Tomography
-
Kuchment, P., & Ong, B.
(2009).
On guided electromagnetic waves in photonic crystal waveguides
-
Agranovsky, M., & Kuchment, P.
(2009).
The support theorem for the single radius spherical mean transform
-
Agranovsky, M., Finch, D., & Kuchment, P.
(2009).
Range conditions for a spherical mean transform
-
Kuchment, P., & Kunyansky, L.
(2009).
Synthetic focusing in ultrasound modulated tomography
-
Kuchment, P.
(2008).
Tight frames of exponentially decaying Wannier functions
-
Kuchment, P.
(2008).
Quantum graphs: an introduction and a brief survey
-
Fulling, S. A., Kuchment, P., & Wilson, J. H.
(2007).
Index theorems for quantum graphs
-
Agranovsky, M., Kuchment, P., & Kunyansky, L.
(2007).
On reconstruction formulas and algorithms for the thermoacoustic tomography
-
Agranovsky, M., & Kuchment, P.
(2007).
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography
-
Kuchment, P., & Kunyansky, L.
(2007).
Mathematics of thermoacoustic tomography
-
Harrison, J. M., Kuchment, P., Sobolev, A., & Winn, B.
(2007).
On occurrence of spectral edges for periodic operators inside the Brillouin zone
-
Kuchment, P., & Post, O.
(2006).
On the spectra of carbon nano-structures
-
Agranovsky, M., Kuchment, P., & Quinto, E. T.
(2006).
Range descriptions for the spherical mean Radon transform
-
Kuchment, P.
(2006).
Integral representations of solutions of periodic elliptic equations
-
Kuchment, P., & Vainberg, B.
(2005).
On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators
-
Ambartsoumian, G., & Kuchment, P.
(2005).
A range description for the planar circular Radon transform
-
Fulling, S. A., & Kuchment, P.
(2005).
Coincidence of length spectra does not imply isospectrality
-
Kuchment, P., & Pinchover, Y.
(2005).
Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds
-
Kuchment, P.
(2004).
Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
-
Ambartsoumian, G., & Kuchment, P.
(2004).
On the injectivity of the circular Radon transform arising in thermoacoustic tomography
-
Kuchment, P., & Pinchover, Y.
(2000).
Integral representations and Liouville theorems for solutions of periodic elliptic equations
-
Kuchment, P., & Vainberg, B.
(1999).
On absence of embedded eigenvalues for Schrdinger operators with perturbed periodic potentials
-
Kuchment, P., & Levendorski, S.
(1998).
On absolute continuity of spectra of periodic elliptic operators
-
Kuchment, P.
(2023).
Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown
editor of
-
book
-
Bal, G.
(2011).
Tomography and Inverse Transport Theory International Workshop on Mathematical Methods in Emerging Modalities of Medical Imaging, October 25-30, 2009, Banff, Canada : International Workshop on Inverse Transport Theory and Tomography, May 16-21, 2010, Banff, Canada
Kuchment, P. (Eds.),
American Mathematical Soc..
-
Weitsman, M.
(2010).
Spectral Theory and Geometric Analysis
Kuchment, P. (Eds.),
American Mathematical Soc..
-
Exner, P.
(2008).
Analysis on Graphs and Its Applications Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 8-June 29, 2007
Kuchment, P. (Eds.),
American Mathematical Soc..
-
Kuchment, P.
(2003).
Waves in Periodic and Random Media Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Waves in Periodic and Random Media, June 22-28, 2002, Mount Holyoke College, South Hadley, MA
Kuchment, P. (Eds.),
American Mathematical Soc..
-
Quinto, E. T., Cheney, M., Kuchment, P., & Society, A. M.
(1994).
Tomography, Impedance Imaging, and Integral Geometry 1993 AMS-SIAM Summer Seminar on the Mathematics of Tomography, Impedance Imaging, and Integral Geometry, June 7-18, 1993, Mount Holyoke College, Massachusetts
Kuchment, P. (Eds.),
American Mathematical Soc..
-
Berkolaiko, G.
Quantum Graphs and Their Applications Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 19-23, 2005, Snowbird, Utah
Berkolaiko, G. (Eds.),
American Mathematical Soc..
-
Bal, G.
(2011).
Tomography and Inverse Transport Theory International Workshop on Mathematical Methods in Emerging Modalities of Medical Imaging, October 25-30, 2009, Banff, Canada : International Workshop on Inverse Transport Theory and Tomography, May 16-21, 2010, Banff, Canada
Kuchment, P. (Eds.),
American Mathematical Soc..
Research
principal investigator on
- Spectral problems of mathematical physics and material science awarded by Directorate for Mathematical & Physical Sciences - (Arlington, Virginia, United States) 2020 - 2023
- Inverse Problems For Biomedical Imaging and Homeland Security awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2021
- Spectral Problems of Mathematical Physics Related to Novel Materials Science and Photonics awarded by National Science Foundation - (Arlington, Virginia, United States) 2015 - 2018
- Collaborative Research: Mathematics of Emerging Imaging Methods In Medicine and Homeland Security awarded by National Science Foundation - (Arlington, Virginia, United States) 2012 - 2018
Teaching
teaching activities
- MATH200 Horizons Of Mathematics Instructor
- MATH423 Linear Algebra Ii Instructor
- MATH611 Intro Ord & Part Diff Eq Instructor
- MATH612 Part Diff Eq Instructor
- MATH640 Linear Algebra For Appl Instructor
- MATH658 Appl Harm Analysis Instructor
- MATH663 Seminar In Analysis Instructor
- MATH664 Seminar Applied Math Instructor
- MATH677 Math Foundations Data Science Instructor
- MATH685 Directed Studies Instructor
- MATH689 Sptp: Math Found Data Science Instructor
- MATH689 Sptp:professional Prep Instructor
- MATH689 Sptp:teaching Undergraduate M Instructor
- MATH689 Sptp:topological Insulators Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Allmaras, Moritz (2012-02). Modeling Aspects and Computational Methods for Some Recent Problems of Tomographic Imaging.
-
Ambartsoumian, Gaik (2009-06). Spherical radon transforms and mathematical problems of thermoacoustic tomography.
-
Do, Ngoc Thanh (2016-05). Some Spectral Problems in Mathematical Physics.
-
Georgieva-Hristova, Yulia Nekova (2011-10). Mathematical Problems of Thermoacoustic and Compton Camera Imaging.
-
Kha, Minh Tuan (2017-05). Spectral Edge Properties of Periodic Elliptic Operators.
-
Moon, Sunghwan (2013-10). Properties of Some Integral Transforms Arising in Tomography.
-
Nguyen, Linh V. (2010-10). Mathematical Problems of Thermoacoustic Tomography.
-
Ong, Beng Seong (2006-10). Spectral problems of optical waveguides and quantum graphs.
-
Terzioglu, Fatma (2018-02). Compton Camera Imaging and the Cone Transform.
-
Weyand, Tracy Kathleen (2014-07). Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator.
Background
education and training
- D.Sc. in Mathematics, National Academy of Sciences of Ukraine - (Kiev, Ukraine) 1983
- Ph.D. in Mathematics, University of Kharkiv - (Kharkiv, Ukraine) 1973
- M.S. in Mathematics, Voronezh State University - (Voronezh, Russia) 1971
awards and honors
- Fellow of the Society for Industrial and Applied Mathematics, conferred by Society for Industrial and Applied Mathematics - (Philadelphia, Pennsylvania, United States), 2018
- AAAS Fellow, conferred by American Association For The Advancement of Science - (Washington D.C., District of Columbia, United States), 2015
- Senior Member, conferred by IEEE Foundation - (Piscataway, New Jersey, United States), 2015
- Fellow, conferred by American Mathematical Society - (Providence, Rhode Island, United States), 2013
- University Distinguished Professor, conferred by Texas A&M University - (College Station, Texas, United States), 2011
- Fellow, conferred by Institute of Physics - (London, United Kingdom), 2009
Contact
first name
- Peter
has last name
- Kuchment
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- kuchment@tamu.edu