**Xuguang LU ****(****卢旭光****)**

**Postal Address:**

**Department of Mathematical Sciences**

**Tsinghua**** University**

**Beijing**** 100084, P.R. China**

**E-mail: xglu@math.tsinghua.edu.cn**

**Phone: +86-10-62788972**

**Fax: +86-10-62792401**

**Brief Curriculum Vitae**

**Birth Date and Place: Nov. 04, 1955, Liaoning,
**

**BS (1982)
Northern Jiaotong
University, **

**MS (1986) Jilin University,
**

**PhD (1997) Tsinghua University,
**

**Positions at **

**Assistant Professor (1986--1988),**

**Lecturer (1988--1993),**

**Associate Professor (1993--2001),**

**Professor (2001--now).**

**Visiting Experience:**

**Aug. 2001-- Oct. 2001, Visiting Scholar, **

**Nov. 2001-- Nov. 2002, Visiting Scholar, Georgia
Institute of Technology,
**

**Jan. 2006 -- Feb. 2006, Visiting Professor, Université Paris **

**Some places of academic talks given in international meetings and
workshops:**

**Beijing**** (several times since 1995), Atlanta
(1999), Oberwolfach (2003, 2010), Zhenjiang (2004),**

**Shanghai (2005, 2010, 2013), Xining
(2006), Wuhan
(2008, 2009), UCLA(2009).**

**Teaching**

**Calculus, Mathematical Analysis, Real Analysis,
Functional Analysis.**

**Current teaching:
Mathematical Analysis, Sep. 2012--Jan. 2014.**

**Research Interest**

**Current****: Kinetic Theory, Classical and
Quantum Boltzmann Equations; Earlier
: Approximation Theory of Functions.**

**Ludwig Boltzmann (1844--1906), Austrian physicist who established the
relationship between entropy and the statistical analysis **

**of****
molecular motion in 1877, founding the branch of physics known as statistical
mechanics. Boltzmann's statistical interpretation **

**led**** him to
conclude that entropy-decreasing processes were exceedingly improbable but not
absolutely impossible. It also paved **

**the**** way for
the development of quantum mechanics, which is inherently a statistical theory.
Boltzmann argued that the equipartition theorem **

**was**** a
fundamental feature of the kinetic theory. He also derived the "H-theorem " and Boltzmann equation in his paper of 1872. **

**The H-theorem expresses the increase in entropy of an irreversible
process (http://scienceworld.wolfram.com/biography/Boltzmann.html).**

**For more information see the book "Ludwig Boltzmann: The Man Who Trusted
Atoms" written by Carlo Cercignani**

**(Oxford University Press, 1998).**** This book has been
translated into Chinese by Xinhe Hu.**

**Publications**

**[35] X. Lu, The Boltzmann equation for Bose-Einstein particles:
condensation in finite time. J. Stat. Phys. 150 (2013), no. 6,
1138--1176.**

**[34] X. Lu, On backward solutions of the
spatially homogeneous Boltzmann equation for Maxwelian
molecules. J. Stat.
Phys. 147 (2012), no. 5, 991--1006.**

**[33] X. Lu and Clément Mouhot, On measure
solutions of the Boltzmann equation, part I: moment production and stability
estimates. J. Differential Equations
252 (2012), no. 4, 3305-3363.**

**[32] X. Lu and Xiangdong
Zhang, On the Boltzmann equation for 2D Bose-Einstein particles, J. Stat. Phys. 143 (2011), no. 5,
990-1019.**

**[31] Eric A . Carlen, Maria C. Carvalho and X.
Lu, On
strong convergence to equilibrium for the Boltzmann equation with soft
potentials. J. Stat.
Phys. 135 (2009), no. 4, 681--736.**

**[30] X. Lu, On the Boltzmann equation for Fermi-Dirac particles with very
soft potentials: global existence of weak solutions. J. Differential Equations 245 (2008), no. 7, 1705 --1761.**

**[29]X. Lu, On the Boltzmann equation for Fermi-Dirac particles with very
soft potentials: averaging compactness of weak solutions. J. Stat. Phys. 124
(2006), no. 2-4, 517--547.**

**[28]X. Lu, The Boltzmann equation for
Bose-Einstein particles: velocity concentration and convergence to equilibrium. J. Stat. Phys. 119 (2005), no. 5-6, 1027--1067.**

**[27] X. Lu, On isotropic distributional
solutions to the Boltzmann equation for Bose-Einstein particles. J. Statist. Phys. 116 (2004), no. 5-6, 1597--1649.**

**[26] Eric A. Carlen and X. Lu, Fast and slow convergence to
equilibrium for Maxwellian molecules via Wild
sums, J. Statist. Phys. 112
(2003), no. 1-2, 59--134. **

**[25] X. Lu and Bernt Wennberg, On stability
and strong convergence for the spatially homogeneous Boltzmann equation for
Fermi-Dirac particles, Arch. Rational Mech. Anal. 168 (2003), no.1, 1--34. **

**[24] Yingkui Zhang and X. Lu, Boltzmann equations with quantum
effects II. Entropy identity, existence and uniqueness of
spatial decay solutions, Tsinghua Sci.
Technol. 7 (2002), no. 3, 219--222.**

**[23] Yingkui Zhang and X. Lu, Boltzmann equations with quantum effects
I. Long time behavior of spatial decay solutions, Tsinghua
Sci. Technol. 7 (2002), no. 3, 215--218.**

**[22] X. Lu and Bernt Wennberg , Solutions with increasing energy for the
spatially homogeneous Boltzmann equation,
Nonlinear Anal. Real
World Appl. 3 (2002), no. 2, 243--258.**

**[21] X. Lu and Yingkui Zhang, On nonnegativity
of solutions of the Boltzmann equation,
Transport Theory Statist Phys.
30 (2001), no. 7, 641--657.**

**[20] X. Lu,
On spatially homogeneous solutions of a modified Boltzmann
equation for Fermi-Dirac particles,
J. Statist. Phys. 105 (2001), no. 1-2, 353--388.**

**[19] X. Lu,
A modified Boltzmann equation for Bose-Einstein particles:
Isotropic solutions and long-time behavior, J.
Statist Phys. 98 (2000), no.5-6, 1335--1394.**

**[18] X. Lu, Conservation of energy, entropy
identity, and local stability for the spatially homogeneous Boltzmann equation,
J. Statist Phys. 96 (1999), no. 3-4,
765--796.**

**[17] X. Lu, Spatial decay solutions of the Boltzmann equation: converse
properties of long time limiting behavior, **

**[16] X. Lu,
A direct method for the regularity of the gain term in the
Boltzmann equation, J. Math.Anal. Appl. 228 (1998), no. 2, 409--435.**

**[15] X. Lu,
A result on uniqueness of mild solutions of Boltzmann
equations, Proceedings of the Fourteenth
International Conference on Transport Theory (**

**[14] Hongxing Zou, X. Lu, Qionghai
Dai, and Yanda Li, Nonexistence of cross-term free time-frequency
distribution with concentration of Wigner-Ville distribution, Sci. China Ser. F 45 (2002), no. 3,
174--180.**

**[13] X. Lu,
Interpolation inequalities and decay estimates for
derivatives, Approx. Theory Appl. (N.S.) 16 (2000), no. 3, 10--31.**

**[12] Simin He, X. Lu, and Bo Zhang, Performance
evaluation of partition-based initial point strategy in local search, Chinese J. Computers 21 (1998) Suppl.,
73--78. ( in Chinese)**

**[11] Dayong Cai and
X. Lu, On
inhomogeneous eigen problems and pseudospectra
of matrices, Scientific computing (Hong
Kong, 1997), 49--57, Springer, **

**[10] X. Lu,
Series representation of Daubechies'
wavelets, J. Comput.
Math.15 (1997),
no. 1, 81--96.**

**[9] X. Lu,
Markov-Bernstein type inequalities of multivariate polynomials
with positive coefficients and applications, Approx.
Theory Appl. (N.S.) 12 (1996), no. 4, 46--66.**

**[8] X. Lu, A negative result on multivariate convex approximation by
positive linear operators, J. Approx. Theory 86 (1996), no. 1,
108--119.**

**[7] X. Lu,
Matrix inhomogeneous eigenvalue
analysis, (Chinese) Math. Numer. Sinica 16 (1994), no. 3, 319--332; translation in Chinese J. Numer. Math. Appl. 16
(1994), no. 4, 75--91. **

**[6] X. Lu, On shape preserving extension and approximation of functions, Approx. Theory Appl.
8 (1992), no. 2, 67--88.**

**[5] X. Lu, On $L\sb
1$-mean approximation to convex functions by positive linear operators, Approximation, optimization and computing,
143--146, North-Holland, **

**[4] X. Lu, Convex approximation by
multivariate polynomials, (Chinese) Math.
Numer.
Sinica
12 (1990), no. 2, 186--193; translation in
Chinese J. Numer. Math. Appl. 12 (1990), no. 3, 59--69.**

**[3] Renhong Wang
and X. Lu, On
dimensions of spaces of bivariate splines
with triangulations, Sci. China Ser. A. 32 (1989), no. 6,
674--684.**

**[2] X. Lu, On shape preserving approximation
by multivariate positive linear operators,
J. Tsinghua Univ. 28 (1988), No. S6, 93-101 (in Chinese).**

**[1] X. Lu, On the order of Bernstein
polynomial approximation of multivariate convex functions, (Chinese) Math. Numer. Sinica 10 (1988), no. 4, 398--407; translation in Chinese J. Numer. Math. Appl. 11 (1989), no. 1, 33--42.**