ICTI: CMU-Portugal Program in Applied Mathematics

Research, PhD and Postdoc Training in Applied Analysis,Probability and Stochastic Analysis

http://icti.math.cmu.edu/index.html

Faculty

Because of their common scientific themes, the ICTI programfunctions within the CNA, Center for Nonlinear Analysis

http://www.math.cmu.edu/cna/index.html

Since 1991; now funded by the National Science Foundation

• Management:Irene Fonseca (PI), Director (Calculus of Variations, PDEs)David Kinderlehrer (PDEs)Giovanni Leoni (Calculus of Variations)Robert Pego (Co-PI), Associate Director (PDEs)Noel Walkington (Numerical Analysis of PDEs)

• Other Permanent Faculty Include: Dejan Slepcev (PDEs),Kavita Ramanan (Probability), Shlomo Ta’asan (ScientificComputing)

Faculty

Because of their common scientific themes, the ICTI programfunctions within the CNA, Center for Nonlinear Analysis

http://www.math.cmu.edu/cna/index.html

Since 1991; now funded by the National Science Foundation

• Management:Irene Fonseca (PI), Director (Calculus of Variations, PDEs)David Kinderlehrer (PDEs)Giovanni Leoni (Calculus of Variations)Robert Pego (Co-PI), Associate Director (PDEs)Noel Walkington (Numerical Analysis of PDEs)

• Other Permanent Faculty Include: Dejan Slepcev (PDEs),Kavita Ramanan (Probability), Shlomo Ta’asan (ScientificComputing)

Current Postdocs

• Filippo Cagnetti, 2008-2009 (ICTI)Ph.D. 2007, SISSA-TriesteMentors: Irene Fonseca and Giovanni Leoni

• Milena Chermisi, 2008-2009 (ICTI)Ph.D. 2007, U. Roma IMentors: Irene Fonseca and Giovanni Leoni

• Marco Barchiesi, 2007-2009Ph.D. 2007, SISSA - TriesteMentors: Irene Fonseca and Giovanni Leoni

• Elaine Cozzi, 2007-2010Ph.D. 2007, University of Texas at AustinMentor: Robert Pego

• Yekaterina Epshtein, 2007-2010Ph.D. 2007, University of PittsburghMentors: David Kinderlehrer and Shlomo Ta’asan

Current Postdocs

• Filippo Cagnetti, 2008-2009 (ICTI)Ph.D. 2007, SISSA-TriesteMentors: Irene Fonseca and Giovanni Leoni

• Milena Chermisi, 2008-2009 (ICTI)Ph.D. 2007, U. Roma IMentors: Irene Fonseca and Giovanni Leoni

• Marco Barchiesi, 2007-2009Ph.D. 2007, SISSA - TriesteMentors: Irene Fonseca and Giovanni Leoni

• Elaine Cozzi, 2007-2010Ph.D. 2007, University of Texas at AustinMentor: Robert Pego

• Yekaterina Epshtein, 2007-2010Ph.D. 2007, University of PittsburghMentors: David Kinderlehrer and Shlomo Ta’asan

More Current Postdocs

• Jason Howell, 2007-2010Ph.D. 2007, Clemson UniversityMentor: Robert Pego

• Stefan Kroemer, 2008-2010Ph.D. 2007, University of AugsburgMentor: Irene Fonseca

• Ana Margarida Ribeiro, 2007-2008Ph.D. 2006, EPFL - LausanneMentor: Irene Fonseca

• Richard Sharp, 2007-2009Ph.D. 2005, Princeton UniversityMentors: David KInderlehrer and Shlomo Ta’asan

Former Postdocs

Central to CNA: graduate education and postdoctoral training

Rustum Choksi (Simon Fraser), Antonio De Simone (SISSA),Georg Dolzmann (U. Maryland and U. of Regensburg), MariaEmelianenko (George Mason), Gero Friesecke (U. of Warwickand U. of Munich), Wilfrid Gangbo (Georgia Tech), RobertJerrard (U. of Toronto), Michal Kowalczyk (U. Chile), GiovanniLeoni (CMU), Chun Liu (Penn State), Vincent Millot (U.Cergy-Pontoise), Massimiliano Morini (SISSA), Stefan Muller

(Director, Max Planck Institute for Mathematics in the Sciences,Leipzig), Felix Otto (Director, Hausdorff Center for Mathematics,U. of Bonn), Konstantina Trivisa (U. of Maryland).

The CNA Footprint

leadership in the areas of Calculus of Variations and PDEs;

worldwide asset in the education of young investigatorscognizant of research opportunities at the broad interfacebetween mathematics and physical sciences and engineering;

well poised to identify cutting-edge mathematical questions inscience and engineering, including materials science andbiotechnology;

engaged in the development of international partnerships andcooperation agreements, which play a vital part in the CNAprogram and in the enhancement of the scientific training andresearch activities of the Center.

The CNA Footprint

leadership in the areas of Calculus of Variations and PDEs;

worldwide asset in the education of young investigatorscognizant of research opportunities at the broad interfacebetween mathematics and physical sciences and engineering;

well poised to identify cutting-edge mathematical questions inscience and engineering, including materials science andbiotechnology;

engaged in the development of international partnerships andcooperation agreements, which play a vital part in the CNAprogram and in the enhancement of the scientific training andresearch activities of the Center.

The CNA Footprint

leadership in the areas of Calculus of Variations and PDEs;

worldwide asset in the education of young investigatorscognizant of research opportunities at the broad interfacebetween mathematics and physical sciences and engineering;

well poised to identify cutting-edge mathematical questions inscience and engineering, including materials science andbiotechnology;

engaged in the development of international partnerships andcooperation agreements, which play a vital part in the CNAprogram and in the enhancement of the scientific training andresearch activities of the Center.

The CNA Footprint

leadership in the areas of Calculus of Variations and PDEs;

worldwide asset in the education of young investigatorscognizant of research opportunities at the broad interfacebetween mathematics and physical sciences and engineering;

well poised to identify cutting-edge mathematical questions inscience and engineering, including materials science andbiotechnology;

engaged in the development of international partnerships andcooperation agreements, which play a vital part in the CNAprogram and in the enhancement of the scientific training andresearch activities of the Center.

Research: Imaging

Inpainting (recolorization)

Frescoes of Andrea Mantegna, Ovetari Chapel of the

Eremitani’s Church, Padova (Italy); destroyed by

bombing in WWII

Z

Ωφ(∇u) dx+λ

Z

D|L(u)−v|

pdx+µ

Z

Ω\D|u−u|

pdx

Research: Foams

Surf(ace) Act(ive) A(ge)nt

Fε(u, ρ) :=

∫

Ω

(

1

εf (u) + ε|∇u|2 + ε (ρ − |∇u|)

2

)

dx+β(ε)

∫

Ω

|∇ρ|2 dx

Epitaxially Strained Crystalline Films

F (u,Ωh) :=

∫

Ωh

W (E (u) (x) − E0 (y)) dx +

∫

Γh

ϕ0 (y) dH1 (x) ,

Research: Interface with Materials Science

Interfacial energies in evolving networks; coarsening processes,texture distributions

m i s o r i e n t a t i o n a n g l e 0 . 8 0 . 6 0 . 4 0 . 2 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0energy 1 . 0 0 01 . 0 0 11 . 0 0 21 . 0 0 31 . 0 0 41 . 0 0 51 . 0 0 6 p op ulation0 . 3 50 . 4 00 . 4 50 . 5 00 . 5 50 . 6 00 . 6 50 . 7 00 . 7 50 . 8 0S h a l l o w W e l l : s i m u l a t i o nshallow-well energy den-sity displaying a flattenedwell energy (red) and abimodal GBCD (blue)consistent with experi-mental picture (CMU MRSEC)

More:Grain boundaries

Orientation imaging mi-croscope of (Ni) nickelscale: grains are diame-ter = 200 microns(CMU MRSEC)

Research: Fokker-Planck, Mass Transport, cont.

Molecular motors and brownian rachets to model eukaryoticintracellular transport

simulation of an ensemble ofkinesin-1 molecular motors illus-trating conditions that favor trans-port. Shown exponential decay ispredicted by the theory

0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

7

8

9

X

i=1,...,n

ρi (x + λ) ≦ C0e− C

σ

X

i=1,...,n

ρi (x), x ∈ Ω, x < 1 − λ, where λ = period

Research: Constrained Stochastic Processes

Skorokhod problem (SP) with SP for a stochastic networkoblique reflection field

Gd

d

d

1

2

3

n

n

n

1

3

2

d 0

Dirichlet process characterization of a large class of reflected diffusions Z :

Z = M + A

M martingale and A a “zero energy” process; enables calculation of functionalsof non-semimartingale reflected diffusions, using a generalized Ito’s formula

Research: Mesh Generation Algorithms

Liquid crystals, polymer and biological fluids

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Section Through z = 0

Time = 0.0000

Research: Complex Materials

Three dimensional meshing algorithms are under development

Research: Mathematical Biology

Immune Response

Mathematical modeling of immune response to biodefensepathogens

A

pivotal player in the immune system - a dendritic cell

Main CNA Activities

advanced topics courses

working groups

workshops and conferences

visitors program

seminar series

scientific report series

summer schools

outreach: Summer Undergraduate Applied MathematicsInstitute (SUAMI)

interchange, mobility and internationalization

Advanced Topics Courses

Targeted to graduate students and postdoctoral fellows.Material research oriented, forefront research topics.

• Calculus of Variations in Sobolev Spaces - Fall 2007, Irene

Fonseca

• Geometric Measure Theory and Fine Properties of

Functions - Spring 2008, Nicola Fusco

• Convex Analysis - Spring 2008, Giovanni Leoni

• Optimal Transport, Gradient Flows, and Applications -Spring 2008, Dejan Slepcev

Advanced Topics Courses

Targeted to graduate students and postdoctoral fellows.Material research oriented, forefront research topics.

• Calculus of Variations in Sobolev Spaces - Fall 2007, Irene

Fonseca

• Geometric Measure Theory and Fine Properties of

Functions - Spring 2008, Nicola Fusco

• Convex Analysis - Spring 2008, Giovanni Leoni

• Optimal Transport, Gradient Flows, and Applications -Spring 2008, Dejan Slepcev

Working Groups

CNA mentors, invited researchers, postdocs and graduate students.Working Groups meet weekly . . . “brown bag” lunch setting

• Complex Fluids and Transport- Fall 2007Organizers: Robert Pego and Noel Walkington

• Grain Evolution- Fall 2007Organizers: David Kinderlehrer and Shlomo Ta’asan

• Recent Methods in the Calculus of Variations- Spring 2008Organizers: Irene Fonseca, Nicola Fusco and Giovanni Leoni

Working Groups

CNA mentors, invited researchers, postdocs and graduate students.Working Groups meet weekly . . . “brown bag” lunch setting

• Complex Fluids and Transport- Fall 2007Organizers: Robert Pego and Noel Walkington

• Grain Evolution- Fall 2007Organizers: David Kinderlehrer and Shlomo Ta’asan

• Recent Methods in the Calculus of Variations- Spring 2008Organizers: Irene Fonseca, Nicola Fusco and Giovanni Leoni

Workshops and Conferences

Young researchers are invited to present contributed talks that runon parallel sessions, and are encouraged to apply for financialsupport.

Frontiers of Applied Analysis

Douglas ArnoldHenri BerestyckiHaim BrezisEmmanuele DiBenedettoWeinan EIvar EkelandWilli JagerBarbara KeyfitzGregory LawlerFang-Hua LinPierre-Louis LionsAndrew MajdaHiroshi MatanoLouis NirenbergStanley Osher

Frontiers of Applied Analysis

The list of speakers includes:Douglas Arnold (University of Minnesota)Henri Berestycki (École des Hautes Études en Sciences Sociales)Haim Brezis (Rutgers University)Emmanuele DiBenedetto (Vanderbilt University)Weinan E (Princeton University)Ivar Ekeland (Pacific Institute for the Mathematical Sciences, Vancouver)Willi Jäger (University of Heidelberg)Barbara Keyfitz (Fields Institute)Gregory Lawler (Cornell University)Fang-Hua Lin (Courant Institute)Pierre-Louis Lions (Collège de France)Andrew Majda (Courant Institute)Hiroshi Matano (University of Tokyo)Louis Nirenberg (Courant Institute)Stanley Osher (University of California, Los Angeles)

Advanced undergraduate students, graduate students, and postdoctoral fellows are encouraged to apply for financial support. The deadline for applications is June 15, 2005.

Graduate students, postdocs and scientists with a recent Ph.D. degree are encouraged to contribute a presentation for this conference. The deadline for submission of contributed abstracts is June 30, 2005.

http://www.math.cmu.edu/cna

Organizers: Irene Fonseca, David Kinderlehrer, Roy Nicolaides, Robert Pego, Shlomo Ta’asan

This conference is sponsored by the National Science Foundation, the Office of Naval Research, the Office of Naval Research Global, and the Department of Mathematical Sciences at Carnegie Mellon University.

A Conference on the Occasion of the 15th Anniversary of the Center for Nonlinear Analysis

Carnegie Mellon University, Pittsburgh, PA

September 8–10, 2005

Carnegie Mellon Univ

ersit

y

A Brownian motion path on the plane,

by G

rego

ry F

. Law

ler.

Two-phased incompressible Navier-Stokes splash using O

sh

er-Se

thian

leve

l set

met

hod,

by

R. F

edkiw

e

t al.

A crystallite from a 3D grain growth simula

tion,

D. Kin

derle

hrer

, S. T

a’as

an e

t al

.

Andrew Carnegie, founder of C

arneg

ie M

ello

n U

nive

rstiy

Pittsburgh, PA

US-Chile Workshops: New Developments in Partial

Differential Equations I

Xinfu ChenGianni Dal MasoJuan DavilaManuel Del PinoJean DolbeaultPatricio FelmerIrene FonsecaMarta Garcia-HuidobroIgnacio GuerraDavid KinderlehrerMike KowalczykGiovanni LeoniRaul ManasevichJuan ManfrediSalome MartinezAlexander QuaasPhilippe SoupletCecilia Yarur

Workshop: New Trends in Calculus of Variations and Mass

Transport

Alberto BressanAlmut BurchardIrene FonsecaNicola FuscoPiotr HajlasTadeusz IwaniecRobert JerrardDavid KinderlehrerPekka KyskelaJan MalyRobert McCannMassimiliano MoriniJani OnninenAldo PratelliDejan Slepcev

Alberto Bressan, Penn State UniversityAlmut Burchard, University of Toronto, Toronto, Canada

Irene Fonseca, Carnegie Mellon UniversityNicola Fusco, University of Naples, Naples, Italy

Piotr Hajlasz,

Tadeusz Iwaniec, Syracuse UniversityRobert Jerrard, University of Toronto, Toronto, Canada

David Kinderlehrer, Carnegie Mellon University

Pekka Koskela, University of Jyväaskyläa, Jyväaskyläa, Finland

Jan Malý, Charles University, Prague, Czech RepublicRobert McCann, University of Toronto,

Toronto, CanadaMassimiliano Morini, SISSA,

Trieste, ItalyJani Onninen, Syracuse University

Aldo Pratelli, University of Pavia, Pavia, ItalyDejan Slepčev, Carnegie Mellon University

Center for Nonlinear AnalysisCarnegie Mellon University

Department of Mathematical Sciences

and the National Science Foundation.

Nicola Fusco and Giovanni Leoni

2001 Summer School: Multiscale Problems in Nonlinear

Analysis

Gianni Dal MasoIrene FonsecaRichard JamesDavid KinderlehrerShlomo Ta’asanLuc TartarLev TruskinovskyNoel WalkingtonDieter Wolf

2004 Summer School: Advances in Nonlinear Analysis

Luigi AmbrosioMaria-Carme CaldererWilfrid GangboNassif GhoussoubIrene FonsecaStefan Muller

2006 Summer School: Probabilistic and Analytical

Perspectives on Contemporary

Krzysztof BurdzyCarlos KenigRicardo NochettoPanagiotis SouganidisSrinivasa Varadhan

2006 CNA Summer SchoolProbabilistic and Analytical Perspectives on Contemporary PDEs

Center for Nonlinear Analysis

Carnegie Mellon University, Pittsburgh, PA

May 29 – June 6, 2006

Graduate students and postdocs are encouraged to contribute a presentation for this conference. The deadline for submission of contributed abstracts is March 1, 2006.

Advanced undergraduate students, graduate students, and postdoctoral fellows are encouraged to apply for financial support. The deadline for applications is March 15, 2006.

Center for Nonlinear Analysis

Carnegie Mellon UniversityDepartment of Mathematical SciencesPittsburgh, PA 15213Telephone: 412-268-2545Fax: 412-268-6380email: cn0s@math.cmu.edu http://www.math.cmu.edu/cna/Summer06

Topics will cover:

Essential uses of probability in analysis

Quantitative unique continuation for elliptic, parabolic

and dispersive equations, and applications

Adaptive finite element methods for elliptic PDEs

Fully nonlinear stochastic partial differential equations

and applications

Interacting particle systems and their scaling limits

List of lecturers:

Krzysztof Burdzy, University of WashingtonCarlos Kenig, University of Chicago

Ricardo Nochetto, University of MarylandPanagiotis Souganidis, University of Texas at Austin

Srinivasa Varadhan, New York University

Organizers:

Irene Fonseca, Giovanni Leoni,Robert Pego, Kavita Ramanan

This conference is sponsored by the National Science Foundation and the Department of Mathematical Sciences at Carnegie Mellon University.

2008 Summer School: Contemporary Topics in Nonlinear

PDEs

Ivar EkelandRobert KohnClaude Le BrisFelix OttoBenoit Perthame

and

Goran PeskirAlbert Shiryaev

2008 CNA Summer SchoolContemporary Topics in Nonlinear PDEs

Center for Nonlinear Analysis

Carnegie Mellon University, Pittsburgh, PA

May 29 – June 7, 2008

Graduate students and postdocs are encouraged to contribute a presentation for this conference. The deadline for submission of contributed abstracts is March 1, 2008.

Advanced undergraduate students, graduate students, and postdoctoral fellows are encouraged to apply for financial support. The deadline for applications is March 15, 2008.

Center for Nonlinear Analysis

Carnegie Mellon UniversityDepartment of Mathematical SciencesPittsburgh, PA 15213Telephone: 412-268-2545Fax: 412-268-6380email: cn0s@math.cmu.edu

Lecturers and Topics:

Ivar Ekeland, University of British Columbia Demand functions and the structure of economic theory

Robert Kohn, Courant Institute, New York University Energy-driven pattern formation

Claude Le Bris, École Nationale des Ponts et Chaussées From molecular theories to continuum elasticity: a possible track

Felix Otto, University of Bonn Some PDE problems from materials science

Benoit Perthame, Université Pierre et Marie Curie Growth processes and physiologically structured dynamics

The Summer School will be held concurrently with the “Heath Lectures on Probability and

Mathematical Finance” given byGoran Peskir, University of Manchester and

Albert Shiryaev, Moscow University.

Organizers:

Irene Fonseca, David Kinderlehrer,Dmitry Kramkov, Giovanni Leoni,

Robert Pego, Dejan Slepcev,Shlomo Ta’asan, Noel Walkington

This conference is sponsored by the Department of Mathematical Sciences and Center of Computational Finance at Carnegie Mellon University and the National Science Foundation.

http://www.math.cmu.edu/cna/Summer08 A grain of brass, diameter about 1 cm, separated from

an ingot. From the collection of W.W. Mullins.

Simulation of singularities in a nematic liquid crystal. Director filed superimposed

upon the view through cross polarizers (Walkington).

Model of coarsening in thin liquid films; a configuration early in the coarsening stage (Otto, Rump, and Slepcev).

ˇ

−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Section Through z = 0

Time = 0.0000

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

Networking

Searching for new opportunities, facilitating already existingcollaborations, and fostering the building of new bridges acrossdifferent institutions in the US and in Europe.

International School for Advanced Studies (SISSA) in TriesteEuropean TMR on Phase Transitions on Crystalline Solids.Italy, France, UK, Germany, and The NetherlandsPIMS (Pacific Institute for the Mathematical Sciences,Vancouver, Canada, and the Banff International ResearchStation)Max Planck Institute for Mathematics in the Sciences inLeipzig, GermanyThe Mathematical Institute at the University of Oxford

2002 Agreement on Cultural Cooperation (graduate studentsand research faculty mobility and interchange) with theUniversities of Firenze (Italy), Roma Tor Vergata (Italy),University Louis Pasteur in Strasbourg (France),

A great opportunity!

Get involved!

Encourage your students to apply !!!