Topological invariants through scattering theory and noncommutative geometry
Official website from Nagoya University
Contact:
Serge Richard (richard@math.nagoyau.ac.jp), Rm. 247 in Sci. Bldg. A, Nagoya University

Aim :
1) Study topological invariants of physical systems through scattering theory and noncommutative geometry
2) Provide a challenging environment where students can learn current physics and mathematics simultaneously

Members :
S. Richard (PI), Graduate school of mathematics, Nagoya University
Y. Kawaguchi, Department of applied physics, Nagoya University
Y. Tanaka, Department of applied physics, Nagoya University
H. Moriyoshi, Graduate school of mathematics, Nagoya University

Students involved in the research program :
T. Tatsuno (B4), Department of mathematics, Nagoya University
C. Sun (B4), Department of physics, G30 program, Nagoya University
X. Chen (M2), Graduate school of mathematics, Nagoya University
L. Zhang (B2, B3, B4), Department of physics, G30 program, Nagoya University
Q. Nguyen (B2, B3), School of engineering, G30 program, Nagoya University
N. Tsuzu (B3, B4, M1, M2), Graduate school of mathematics, Nagoya University
S. H. Nguyen (B2, B3, B4), Department of physics, G30 program, Nagoya University
D. Cong Bui (B3), Department of automotive engineering, G30 program, Nagoya University
S. Voleti (B4), Department of applied physics, G30 program, Nagoya University
H. Inoue (M2, D1, D2,D3), Graduate school of mathematics, Nagoya University
D. Parra (Postdoc), Santiago de Chili

Educational activities :
Differential equations and dynamical systems, Fall 2021
Master course on Graphs and epidemiology, Spring 2021
Introduction to probability, Spring 2021
Graph theory, Spring 2020
Master course on Ktheory and cyclic cohomology, Spring 2020
Introduction to functional analysis, Fall 2019
Intensive lecture provided by C. Bourne:
Introduction to Noncommutative Index Theory, Spring 2019:
notes (taken by Hideki Inoue),
homework,
pictures I,
II
Master course on operator theory, Spring 2019
Lectures on statistics, Spring 2019
Lectures on differential geometry, Fall 2018
Master course on scattering theory, Spring 2018
Lectures on groups and their representations, Spring 2018
Lectures on probability, Fall 2017
Seminar on diffraction, Fall 2017

Invitations to Nagoya :
R. Tiedra de Aldecoa, from Dec. 14, 2019 to Jan. 14, 2020
D. Parra, from Oct. 22 to Oct. 24, 2019
T. Umeda, from September 24 to September 25, 2019
Y. Matsuzawa, September 25, 2019
H. Fukaya, September 25, 2019
T. Natsume, September 25, 2019
Y. Tanaka, September 25, 2019
A. Suzuki, September 25, 2019
Y. Tanaka, from July 16 to July 17, 2019
C. Bourne, from May 19 to May 25, 2019
M. Lein, from May 8 to May 11, 2019
A. Drouot, from Feb. 27, 2019 to March 4, 2019
D. Parra, from Feb. 27, 2019 to March 6, 2019
R. Tiedra de Aldecoa, from Dec. 29, 2018 to Jan. 27, 2019
C. Bourne, from Dec. 11 to Dec. 14, 2018
P. Miranda, from Sept. 16 to Sept. 19, 2018
D. Parra, from Sept. 9 to Sept. 19, 2018
J. Faupin, from June 27 to July 5, 2018
C. Bourne, from Apr. 5 to Apr. 10, 2018
H. Obuse, from Apr. 5 to Apr. 7, 2018
M. Lein, from Apr. 5 to Apr. 7, 2018
Y. Ogata , April 6, 2018
M. Sato , April 6, 2018
J.C. Cuenin, from Feb. 18 to Mar. 3, 2018
F. Nicoleau, from Feb. 18 to Mar. 24, 2018
D. Parra, from Jan. 29 to Feb. 12, 2018
R. Tiedra de Aldecoa, from Jan. 23 to Feb. 17, 2018
K. Iohara, from Nov. 8 to Nov 11, 2017

Supported or partially supported outcomes :
1) Publications:
 Q. Sun, T. Miyoshi, S. Richard
Analysis of COVID19 in Japan with Extended SEIR model and ensemble Kalman filter,
submitted.
 C. Sun, T. Miyoshi, S. Richard
Agentbased model and data assimilation: Analysis of COVID19 in Tokyo
submitted.
 S. Richard, R. Tiedra de Aldecoa
Decay estimates for unitary representations with applications to continuous and discretetime models,
submitted.
 S. Richard, N. Tsuzu,
Spectral and scattering theory for topological crystals perturbed by infinitely many new edges,
submitted.
 S. Richard,
Discrete Laplacian in a halfspace with a periodic surface potential: an overview of analytical investigations,
RIMS Kokyuroku 2195 (2021), 18  26.
 S. Richard, Q. Sun, Bibliometric analysis on mathematics, 3 snapshots: 2005, 2010, 2015,
Electron. J. App. Stat. Anal. 14 (2021), 90  116.
 S. Richard, R. Tiedra de Aldecoa, L. Zhang
Scattering operator and wave operators for 2D Schroedinger operators with threshold obstructions,
Complex Anal. Oper. Theory 15, article 106 (2021), 25 pages.
 J. Derezinski, J. Faupin, Q.N. Nguyen, S. Richard
On radial Schroedinger operators with a Coulomb potential: General boundary conditions,
Advances in Operator Theory 5 (2020), 1132  1192.
 S. H. Nguyen, S. Richard, R. Tiedra de Aldecoa,
Discrete Laplacian in a halfspace with a periodic surface potential I:
Resolvent expansions, scattering matrix, and wave operators,
to appear in Mathematische Nachrichten, 2021.
 S. Richard, R. Tiedra de Aldecoa,
Commutator criteria for strong mixing II. More general and simpler,
CUBO 21 (2019), 37  48.
 S. Richard, T. Umeda, On some integral operators appearing in scattering theory,
and their resolutions, in Spectral Theory and Mathematical Physics, 243  256, Latin American Mathematics Series, Springer, 2020.
 G. De Nittis, M. Moscolari, S. Richard, R. Tiedra de Aldecoa,
Spectral and scattering theory of onedimensional coupled photonic crystals, Rev. Math. Phys. 33 (2021) 2150027 (40 pages).

S. Richard,
Periodic Schroedinger operators on topological crystals: framework, analytically fibered operator, conjugate operator,
RIMS Kokyuroku 2123 (2019), 51  68.
 H. Inoue, S. Richard,
Topological Levinson's theorem for inverse square potentials: complex, infinite, but not exceptional,
Rev. Roumaine Math. Pures Appl. 64 (2019), 225  250.

S. Richard, A. Suzuki, R. Tiedra de Aldecoa,
Quantum walks with an anisotropic coin II: scattering theory, Lett. Math. Phys. 109 (2019), 61  88.

H. Inoue, S. Richard,
Index theorems for Fredholm, semiFredholm, and almost periodic operators: all in one example, J. Noncommut. Geom. 13 (2019), 1359  1380.

J. Derezinski, S. Richard,
On radial Schroedinger operators with a Coulomb potential, Ann. Henri Poincaré 19 (2018), 2869  2917.
2) Posters:
3) Conferences and Workshops:

Himeji conference on partial differential equations, March 4  5, 2021, on Zoom.
Program:
Eng.,
Jap.

Workshop: Unitary operators: spectral and topological properties, September 29, 2020, on Zoom.
Information and progam,
group pictures
1 and
2,
slides of
Bourget,
Tsutaya.

Meeting on discrete 2D systems and trace formula, October 24, 2019, Nagoya University.

Workshop: Mathematical approach for topological physics (II), September 25, 2019, Nagoya University.
Progam,
Titles and abstracts,
Group picture,
slides of
Kawaguchi,
Fukaya,
Tamura.

Meeting on quantum walks and Witten index, July 16, 2019, Nagoya University.

Himeji conference on partial differential equations, March 4  6, 2019.
Program:
Eng.,
Jap.

Meeting on spectral and scattering theory, February 28, 2019, Nagoya University.

Meeting on bulkboundary correspondence, December 12, 2018, Nagoya University.

Meeting on discrete and magnetic systems, September 18, 2018, Nagoya University.

Seminar of Prof. Tanaka in the Graduate School of mathematics,
June 13, 2018, Nagoya University.

Workshop: Mathematical approach for topological physics (I), April 6, 2018, Nagoya University.
Information and progam,
Titles and abstracts,
Slides of the presentations on request.

Himeji conference on partial differential equations, February 21  22, 2018.
Program:
Eng.,
Jap.
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