ICTP - Scientific Activities

Scientific Activities

Schools, conferences, workshops, and meetings

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Europe/Rome All lessons will be held in English at the Universidad San Francisco de Quito Campus Cumbaya http://www.usfq.edu.ec/Paginas/Inicio.aspx and Escuela Politécnica Nacional https://www.epn.edu.ec/ **DEADLINE for requesting participation is 24 MARCH 2019** Topics: Optimal Control and Applications to Biology Fluid Mechanics Machine Learning Cancer Dynamics Description continued This activity serves as an opportunity to highlight current research topics and real-world applications in applied mathematics. Students exposed to the mini-courses will learn mathematical tools used to efficiently solve real world problems. Specifically, the intention is to highlight the applications of mathematics in other disciplines as well as in industry in an effort to illustrate mathematics as a useful and necessary tool as well as a lucrative career option. Courses aim to address both theoretical aspects as well as real world applications. The courses will be complemented by additional computer lab sessions where students will solve relevant problems and be given an opportunity to run simulations and learn computational skills. In addition, students will be provided with mentoring regarding jobs in industry as well as opportunities for advanced studies in mathematics. Lecturers include: M. S. Aronna, Escola de Matemática Aplicada (FGV), Brazil J. Bedrossian, University of Maryland, U.S.A. R. Cóbe, Sao Paulo State University, Brazil D. Levy, University of Maryland, U.S.A. Organizers: M. Calahorrano, EPN, Ecuador M. G. Delgadino, Imperial College, U.K. D. C. Ramirez, USFQ, Ecuador L. D. Simonelli, ICTP, Italy G. Violini, Emeritus, CIF, Colombia Local Organizer: C. Arezzo, ICTP, Trieste, Italy Quito - Ecuador ICTP pio@ictp.it

Activity

17 Jun 2019 - 28 Jun 2019

@ Quito - Ecuador

Mathematics

1st Latin American School in Applied Mathematics | (smr 3301)

Secretary: Doreen Sauleek

Organizer(s): Marco Calahorrano (EPN), Matias G. Delgadino (Imperial College), Dennis C. Ramirez (USFQ), Lucia Simonelli (ICTP), Galileo Violini (USFQ), ICTP Scientific Contact: Claudio Arezzo

Cosponsor(s): Escuela Politecnica Nacionalepn, Universidad San Francisco de Quito Campus Cumbayausf

Support E-Mail: smr3301@ictp.it

**DEADLINE: 24/03/2019** **DEADLINE: 24/03/2019**

Europe/Rome A growing number of researchers use algebraic geometry in industrial and applied mathematics: applications include biology, coding theory, cryptography, combustion, computational geometry, computer graphics, quantum computing, control theory, geometric design, complexity theory, machine learning, nonlinear PDE, optimization, and robotics. Algebraic Geometry of data clouds - density of cloud data - reach of a manifold and topological data analysis - classical theory of polar classes of a variety - the nearest points to a variety - the EDD degree of a manifold and its properties - the Bottleneck degree of varieties Biochemical reaction networks modeled by mass-action kinetics - basics on reaction networks with mass-action kinetics: biochemical notions, algebraic notions, dynamical notions   - steady state invariants and computational algebraic geometry   - networks with toric steady states   - counting the number of positive steady states and real solutions to polynomial  systems   Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee. Women are particularly encouraged to apply. ICTP ICTP pio@ictp.it

Activity

1 Jul 2019 - 5 Jul 2019

@ ICTP

Mathematics

Trieste Algebraic Geometry Summer School (TAGSS) 2019 - Algebraic Geometry towards Applications | (smr 3306)

Address: Strada Costiera, 11 I - 34151 Trieste (Italy)

Room: Budinich Lecture Hall (LB)

Secretary: Monica Ancuta, Petra Krizmancic

Organizer(s): Valentina Beorchia (Università di Trieste), Ada Boralevi (Politecnico di Torino), Barbara Fantechi (SISSA), Local Organiser: Fernando Rodriguez Villegas

Cosponsor(s): European Mathematical Society (EMS)ems1, International School for Advanced Studies (SISSA)sissa, Ministero dell'istruzione, dell'università e della ricerca (MIUR)miur2, Politecnico di Torinodisma, Universita' degli Studi di Trieste - Dipartimento di Matematica e Geoscienzedmgts, Foundation Compositio Mathematicafcm

**DEADLINE: 03/03/2019**

Europe/Rome The Eastern Africa Universities Mathematics Programme (EAUMP) courtesy of the International Science Programme (ISP) of Sweden; jointly with ICTP, Trieste, Italy; Sida; CIMPA, DAAD, LMS/AMMSI, COMPOSITIO is organizing a three weeks summer School on Algebraic Topology and its Applications to be held at Makerere University, Kampala, Uganda from 15th July to 2nd August, 2019. It is intended that the School will take the audience comprising young academic staff members and advanced graduate students (M.Sc, Ph.D and Postdoctoral Students) of Mathematics from the Eastern African region and beyond. The school is the next one in a series of schools organized under the Eastern African Universities Mathematics Programme (EAUMP). The most recent EAUMP schools were organized in 2015 at Makerere University, Uganda, on Experimental Pure Mathematics; in 2016 at the University of Rwanda on Number Theory; in 2017 at the University of Nairobi on Modern Functional Analysis; and in 2018 at the University of Dar es Salaam on Homological methods in Algebra and Geometry. All the schools are within one of the main aims of EAUMP which is to improve the pure mathematics in the region. The member Universities of the EAUMP are University of Dar es Salaam, Tanzania; University of Nairobi, Kenya; University of Zambia, Zambia; Makerere University, Uganda; University of Rwanda, Rwanda. GOALS OF THE SCHOOL To introduce participants to current trends in Algebraic Topology and its applications, including knot theory and Topological Data Science, and provide research topics for masters and PhD studies. To provide a forum for African mathematicians to interact, exchange ideas and initiate collaborations. Identify talented students for possible PhD programs. To produce digital lecture material for dissemination, which contributes to the training of master students in the Eastern Africa region. STURCTURE AND PROGRAMME As in the years 2013-2017, participants will be asked to submit mini-projects on the material studied at the School, with the best submissions receiving prizes/awards. They will work on their projects after the end of the School and will submit them during the third week of the school. Here is the detailed course plan for the School. Week 1: Introductory courses Course 1: Introductory Topology Lecturers: Balazs Szendroi (University of Oxford) and Venuste Nyagahakwa (University of Rwanda) Description: This course will introduce the basic ideas of topology, starting with an abstract definition of topological space, and treating many examples. Course 2: The Fundamental Group Lecturer: Jean-Baptiste Gatsinzi (Botswana Institute of Science and Technology) Description: The fundamental group is a basic but key algebraic invariant of a topological space. This course will define this group and give some interesting examples of how to compute it. Week 2: Intermediate courses Course 3: Manifolds Lecturer: Claudia Scheimbauer (NTNU, Trondheim) Description: Manifolds provide a very interesting class of examples of topological spaces, of great interest in applications to geometry, physics and elsewhere. This course will introduce this notion with many examples, mainly from dimensions 1, 2 and 3. Course 4: Introduction to persistent homology Lecturer: Ulrike Tillmann (University of Oxford) Description: Persistent homology, a method for computing topological features of a space at different spatial resolutions, will be explained in this course, with a view towards applications. Week 3: Advanced courses Course 5: Introduction to Knot Theory Lecturer: Mehdi Yazdi (University of Oxford) Description: A knot is a tangled piece of rope in the three dimensional space, with the two loose ends glued together. Knot theory asks questions such as: can this knot be untangled by continuously deforming the rope? Are there ways to tell two knots apart? This course will discuss the basic invariants and quantities defined for knots, together with the connection with the theory of 3-dimensional manifolds. Course 6: Topological Data Analysis Lecturer: Vidit Nanda (University of Oxford) Description: Topological data analysis is a recent and fast-growing field providing a set of new topological and geometric tools to infer global features from complex data. This course will give an introduction to this circle of ideas. SCHOOL PARTICIPATION Online application form is available at http://indico.ictp.it/event/8699/, and will close on 28th April, 2019. Alternative request for participation can be done by originating an email to kasozi@cns.mak.ac.ug copied to ssevviiri@cns.mak.ac.ug, szendroi@maths.ox.ac.uk. Only those applicants who will be successful shall be contacted. Letters of invitation will be issued to participants upon request for the processing of travel documents or soliciting for funding. INTERNATIONAL ORGANISING COMMITTEE Leif Abrahamson (University of Uppsala, Sweden), Prof. Bengt-Ove Turesson (Linkoping University, Sweden), Fernando Rodriguez Villegas (ICTP, Italy), Balazs Szendroi (University of Oxford, UK), Patrick Weke (University of Nairobi, Kenya). LOCAL ORGANIZING COMMITTEE David Ssevviiri (Makerere University), Juma Kasozi (Makerere University), John Mango Makerere University), Patrick Weke (University of Nairobi), Jared Ongaro (University of Nairobi), Eunice Mureithi (University of Dar es Salaam), James Makungu (University of Dar es Salaam), Michael Gahirima (UR-CST, Nyarugenge), Wellars Banzi (UR-CST, Nyarugenge), Mubanga Lombe (University of Zambia), Isaac D. Tembo (University of Zambia). Kampala - Uganda ICTP pio@ictp.it

Activity

15 Jul 2019 - 2 Aug 2019

@ Kampala - Uganda

Mathematics

EAUMP - ICTP Summer School on Algebraic Topology and its Applications | (smr 3310)

Secretary: Koutou Mabilo

Organizer(s): Leif Abrahamson (University of Uppsala, Sweden), Bengt-Ove Turesson (Linkoping University, Sweden), Balazs Szendroi (University of Oxford, UK), Fernando Rodriguez Villegas (ICTP, Italy), Patrick Weke (University of Nairobi, Kenya),

Cosponsor(s): Upssala Universityuppsala, CIMPAcimpa2, African Mathematics Millennium Science Initiativeammsi, LMSlns, Foundation Compositio Mathematicafcm, EAUMPeaump, Sweden Sverigesverige, Linköping Universitylinkop, German Academic Exchange Servicedaad, Makerere Universitymak, Maplesoftmaplesoft

LANGUAGE English will be the official language at the School. CURRENCY Local currency is the Uganda Shilling at the foreign exchange rate of US$ 1 = 3,650 UgShs . There are many local Forex bureaus in Kampala, some of them open 24 hours. Banks and Forex bureaus accept traveler’s cheques and major credits cards are accepted at leading hotels, restaurants and super markets. VISA Visa may be required for International visitors to Kampala - Uganda. Please check with the respective local Embassy for details and other requirements. Letters of invitation will be issued to participants upon request for the processing of travel documents. FURTHER INFORMATION Dr. David Ssevviiri, Department of Mathematics, Makerere University Email: ssevviiri@cns.mak.ac.ug Cell phone: +256-778-486571 Dr. John Mango, Department of Mathematics, Makerere University Email: mango@cns.mak.ac.ug Cell phone: +256-772-649455 Dr. Juma Kasozi, Department of Mathematics, Makerere University Email: kasozi@cns.mak.ac.ug Cell phone: +256-782-308010

Europe/Rome The purpose of the School is to expose graduate students and young researchers to a variety of topics, techniques and lines of research of common interest to geometers and physicists. The activity is intended for theoretical physicists and mathematicians with knowledge of Differential geometry and General Relativity. Topics: Black Holes, Modified Gravity Theories, AdS/CFT Correspondence, Einstein Constraint Equations, Mass in General Relativity, Cosmological Solutions. School Lectures: C. CEDERBAUM, University of Tubingen, Germany P. CHRUSCIEL, University of Vienna, Austria M. DAFERMOS, Princeton University, USA and University of Cambridge, UK H. REALL, DAMTP, University of Cambridge, UK R. SCHOEN, University of California Irvine, USA R. WALD, University of Chicago, USA T. WISEMAN, Imperial College London, UK N. YUNES, Montana State University, USA Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee. ICTP ICTP pio@ictp.it

Activity

15 Jul 2019 - 26 Jul 2019

@ ICTP

Geometry , Mathematics , High Energy Cosmology and Astroparticle Physics

ICTP School on Geometry and Gravity | (smr 3311)

Address: Strada Costiera, 11 I - 34151 Trieste (Italy)

Room: Budinich Lecture Hall (LB)

Secretary: Monica Ancuta, Petra Krizmancic

Organizer(s): Lorenzo Mazzieri (Università di Trento, Italy), Richard Schoen (University of California Irvine, USA), Robert Wald (University of Chicago, USA), Local Organisers: Claudio Arezzo, Paolo Creminelli

Cosponsor(s): Italian Institute for Nuclear Physics (INFN)infn

**DEADLINE: 30/04/2019**

Europe/Rome This activity is part of a two-week event consisting of Week 1: School and Workshop on Mixing and Control (16 - 20 September) Week 2: School and Workshop on Random Matrix Theory and Point Processes (23 - 27 September) To participate in both activities you need to submit two distinct applications. Week 1: Please click on the link "Apply here" on the left hand-side column Week 2: Please apply at: http://indico.ictp.it/event/8900/ DEADLINE for requesting participation for both weeks: 15 MAY 2019 ========================================================== Organizers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute T. Grava, SISSA & Bristol A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Local Organizer: S. Luzzatto, ICTP, Trieste The topics to be discussed at the activity are at the forefront of current research in Random Matrix Theory, Point Processes, Dynamical Systems and Control Theory. One of the main goals of the School and Workshop is to bring this material to both established and young mathematicians from all developing countries. Mini courses will be given as well as more advanced reserach seminars. The activity will be organized as two thematic weeks on interrelated topics. Each week will consist of one or two mini courses and some seminar speakers. Week 1: Mixing and Control Mixing and control central topic is the study, with the help of the mathematical control theory, of ergodic and mixing properties of dynamical systems stochastically perturbed by a very degenerate noise. This concerns the systems governed by nonlinear PDEs and ODEs. We also plan to discuss mathematical aspects of the non-equilibrium statistical physics and some other topics. Week 2: Random Matrix Theory and Point Processes The second week will focus on point processes arising in the study of random matrices such as determinantal point processes. These point processes satisfy the Kolmogorov 0-1 Law and the Central Limit Theorem of Soshnikov, are rigid in the sense of Ghosh and Peres and obey an analogue of the De Finetti Theorem. Palm-Khintchine theory for our point processs will be emphasized, as well as the connection with the theory of integrable systems. Numerous open problems will be discussed, in particular, those related to pfaffian point processes. Topics: Point process; Random matrices; Integrable probability; Integrable systems; Mixing; Stationary measure; Markov systems; Nonholonomic constraints; Controllability; Lecturers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Speakers: F. Augeri, Weizmann, Israel F. Baudoin, Purdue Univ. C. Bordenave, Toulose, France U. Boscain, CNRS, Sorbonne Univ. A. Bufetov, MIT M. Cafasso, Angers, France *I. Corwin, Columbia University N. Cuneo, University Paris-Diderot A. de Bouard, Ecole Polytechnique A. Debussche, ENS Rennes A. Dymov, Steklov Insitute, Moscow J-P. Eckmann, University of Geneva *L. Erdoes, Wien, Austria N. Glatt-Holtz, Tulane University H. Guan, Tsinghua University V. Jaksitch, McGill University I. Krasovsky, Imperial College M. Krishnapur, Bangalore, India *A. Kupiainen, University of Helsinki K. Mc Laughlin, Colorado State University V. Nersesyan, University of Versailles P. Nikitin, Steklov, St. Petersburg G. Olshanski, ITP, RAS, Russia S. Peche, LPSM, Paris, France Y. Qiu, CNRS, France A. Ramirez, Pontificia Universidad Catolica de Chile R. Raquepas, University Grenoble Alpes (Institut Fourier) T. Sasamoto, Chiba, Japan M. Shcherbina, Kharkov, Ukraina A. Shirikyan, Cergy-Pontoise N. Tzvetkov, University of Cergy Pontoise A. Veselov, Loughbourogh University *H-T. Yau, Harvard * to be confirmed ICTP ICTP pio@ictp.it

Activity

16 Sep 2019 - 20 Sep 2019

@ ICTP

Mathematics

School and Workshop on Mixing and Control | (smr 3324)

Address: Strada Costiera, 11 I - 34151 Trieste (Italy)

Room: Budinich Lecture Hall (LB)

Secretary: Doreen Sauleek

Organizer(s): A. Agrachev (SISSA, Trieste), A. Bufetov (Marseille and Steklov Institute), T. Grava (SISSA & Bristol), A. Guionnet (ENS, Lyon), S. Kuksin (Paris & Shandong University), Local Organiser: Stefano Luzzatto

Cosponsor(s): SISSAsissa3, NSFnsf2

Support E-Mail: smr3324@ictp.it

**DEADLINE: 15/05/2019**

Europe/Rome Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases. The closely related field of dynamical systems has a much older origin, going back at least to Newtonian mechanics. Both subjects have since flourished into extremely active subjects with connections to many parts of mathematics and the physical sciences. Progress has been especially rapid in the last few years in differentiable dynamics and homogeneous dynamics. Differentiable dynamics studies flows on smooth manifolds and has links with geometry while homogeneous dynamics is the study of subgroup actions on homogeneous spaces of Lie groups and has connections to number theory. It is the aim of this two week workshop to ga ther top experts in these two subjects to deliver expositions on the state of the art in these subjects. The first week will be devoted to differentiable dynamics and the second week to homogeneous dynamics. Special Lectures: Infosys-ICTS Ramanujan lectures - by Elon Lindenstrauss ICTS Distinguished lecture - by Marcelo Viana. List of invited Speakers Speakers week 1: Alex Blumenthal, Maryland, USA Aaron Brown, Chicago, USA Sylvain Crovisier, Paris Sud Carlangelo Liverani, Rome, Italy Federico Rodriguez-Hertz, Penn State, USA Jana Rodriguez-Hertz, Shenzen, China Sebastian van Strien, Imperial College, UK Marcelo Viana, IMPA Khadim War, IMPA, Brazil Zhiyuan Zhang, Princeton Speakers week 2: Victor Beresnevich, University of York S. G. Dani, University of Mumbai Manfred Einsiedler, ETH Zurich Alexander Gorodnik, University of Zurich Seonhee Lim, Seoul National University Elon Lindenstrauss, Hebrew University of Jerusalem Jens Marklof, University of Bristol Shahar Mozes, Hebrew University of Jerusalem Amos Nevo, Technion, Haifa Sanju Velani, University of York Barak Weiss, Tel Aviv University Minicourse Lecturers Sylvain Crovisier, Paris Sud, France Stefano Luzzatto, ICTP Both weeks will feature research talks by leading mathematicians as well as mini courses. A number of slots will be available in the program for younger participants to present their research and a poster session will also be organized. A number of slots will be available in the programme for younger participants to present their research and a poster session will also be organized. The program is jointly organised and supported by ICTS and IMPA. Program link: https://www.icts.res.in/program/etds2019 General Information: https://www.icts.res.in/program/Information-for-Participants Bangalore - India ICTP pio@ictp.it

Activity

23 Sep 2019 - 4 Oct 2019

@ Bangalore - India

Mathematics

School on Smooth and Homogeneous Dynamics | (smr 3271)

Secretary: Koutou Mabilo

Organizer(s): Marcelo Viana (IMPA), Anish Ghosh (TIFR), Stefano Luzzatto (ICTP),

Cosponsor(s): ICTSicts, IMPAimpa

Europe/Rome This activity is part of a two-week event consisting of Week 1: School and Workshop on Mixing and Control (16 - 20 September) Week 2: School and Workshop on Random Matrix Theory and Point Processes (23 - 27 September) To participate in both activities you need to submit two distinct applications. Week 1: Please apply at: http://indico.ictp.it/event/8720/ Week 2: Please click on the link "Apply here" on the left hand-side column DEADLINE for requesting participation for both weeks: 15 MAY 2019 ======================================================= Organizers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute T. Grava, SISSA & Bristol A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Local Organizer: S. Luzzatto, ICTP, Trieste The topics to be discussed at the activity are at the forefront of current research in Random Matrix Theory, Point Processes, Dynamical Systems and Control Theory. One of the main goals of the School and Workshop is to bring this material to both established and young mathematicians from all developing countries. Mini courses will be given as well as more advanced reserach seminars. The activity will be organized as two thematic weeks on interrelated topics. Each week will consist of one or two mini courses and some seminar speakers. Week 1: Mixing and Control Mixing and control central topic is the study, with the help of the mathematical control theory, of ergodic and mixing properties of dynamical systems stochastically perturbed by a very degenerate noise. This concerns the systems governed by nonlinear PDEs and ODEs. We also plan to discuss mathematical aspects of the non-equilibrium statistical physics and some other topics. Week 2: Random Matrix Theory and Point Processes The second week will focus on point processes arising in the study of random matrices such as determinantal point processes. These point processes satisfy the Kolmogorov 0-1 Law and the Central Limit Theorem of Soshnikov, are rigid in the sense of Ghosh and Peres and obey an analogue of the De Finetti Theorem. Palm-Khintchine theory for our point processs will be emphasized, as well as the connection with the theory of integrable systems. Numerous open problems will be discussed, in particular, those related to pfaffian point processes. Topics: Point process; Random matrices; Integrable probability; Integrable systems; Mixing; Stationary measure; Markov systems; Nonholonomic constraints; Controllability. Lecturers: A. Agrachev, SISSA, Trieste A. Bufetov, Marseille & Steklov Institute A. Guionnet, ENS Lyon S. Kuksin, Paris & Shandong University Speakers: F. Augeri, Weizmann, Israel F. Baudoin, Purdue Univ. C. Bordenave, Toulose, France U. Boscain, CNRS, Sorbonne Univ. A. Bufetov, MIT M. Cafasso, Angers, France *I. Corwin, Columbia University N. Cuneo, University Paris-Diderot A. de Bouard, Ecole Polytechnique A. Debussche, ENS Rennes A. Dymov, Steklov Insitute, Moscow J-P. Eckmann, University of Geneva *L. Erdoes, Wien, Austria N. Glatt-Holtz, Tulane University H. Guan, Tsinghua University V. Jaksitch, McGill University I. Krasovsky, Imperial College M. Krishnapur, Bangalore, India *A. Kupiainen, University of Helsinki K. Mc Laughlin, Colorado State University V. Nersesyan, University of Versailles P. Nikitin, Steklov, St. Petersburg G. Olshanski, ITP, RAS, Russia S. Peche, LPSM, Paris, France Y. Qiu, CNRS, France A. Ramirez, Pontificia Universidad Catolica de Chile R. Raquepas, University Grenoble Alpes (Institut Fourier) T. Sasamoto, Chiba, Japan M. Shcherbina, Kharkov, Ukraine A. Shirikyan, Tzvetkov, University of Cergy Pontoise A. Veselov, Loughbourogh University *H-T. Yau, Harvard * to be confirmed PLEASE NOTE: Additional funds are available for participants based in the US through the National Science Foundation. Please complete and submit the application at the following link in ADDITION to the regular online request for participation to the activity. https://www.dropbox.com/s/m0ra2m0j2oomz2s/NSF_application.docx?dl=0 ICTP ICTP pio@ictp.it

Activity

23 Sep 2019 - 27 Sep 2019

@ ICTP

Mathematics

School and Workshop on Random Matrix Theory and Point Processes | (smr 3382)

Address: Strada Costiera, 11 I - 34151 Trieste (Italy)

Room: Budinich Lecture Hall (LB)

Secretary: Doreen Sauleek

Organizer(s): A. Agrachev (SISSA, Trieste), A. Bufetov (Marseille and Steklov Institute), T. Grava (SISSA, Trieste), A. Guionnet (ENS, Lyon), S. Kuksin (Paris & Shandong University), Local Organiser: Stefano Luzzatto

Cosponsor(s): SISSAsissa3, NSFnsf2

Support E-Mail: smr3324@ictp.it

**DEADLINE: 15/05/2019**

Europe/Rome The main focus is on recent developments in gauge theories, both in theoretical physics and in mathematics. This area is very fruitful for active interplays between Mathematics and Physics. In theoretical physics exact results in supersymmetric quantum field theories and superstrings on curved backgrounds prompted the interest in explicit calculations of (equivariant) Donaldson invariants also in higher rank and the possible definition of new invariants for four manifolds using non-Lagrangian theories. On the mathematical side, new results have been obtained for higher rank Donaldson invariants and Vafa-Witten invariants. A key role is played by the interplay of with representation theory and quantum integrable systems. These developments are also expected to have impact on enumerative geometry, knot theory and representation theory of infinite dimensional algebras. A key technical tool in these developments is equivariant localization which allows the extraction of exact results. Topics : higher rank Donaldson invariants Vafa-Witten invariants Donaldson-Thomas invariants study of the BPS spectra of (non Lagrangean) N=2 Gauge Theories and new four-dimensional invariants relation to matrix models and topological strings quantum Hitchin systems and character varieties gauge theories on complex toric surfaces and their instanton moduli spaces surface operators in gauge theory and moduli spaces of principal bundles with parabolic structure quantum cohomology of the instanton moduli space K-theory of quiver varietes quantum integrability, quantum Yang-Baxter equations relations to knot theory and Khovanov Homology higher dimensional supersymmetric gauge theories and M-theory Lecturers: L. GÖTTSCHE, ICTP G. MOORE, Rudgers (tbc) H. NAKAJIMA, Kavli IPMU N. NEKRASOV, Simons Center (tbc) P. PUTROV, ICTP Speakers include: A. DAEMI, Simons Center A. GOLAMPOUR, University of Maryland S. GUKOV, Caltech S. JEONG, Stony Brook A. KLEMM, Universität Bonn M. KOOL, Utrecht University J. MANSCHOT, Trinity College Dublin A. MELLIT, Universität Wien D. OPREA, University of California, San Diego D. PEI, Caltech Z. RUIDONG, Tokyo University A. SHESHMANI, Harvard University Y. TANAKA, Oxford University K. YOSHIOKA, Kobe Unversity ICTP ICTP pio@ictp.it

Activity

30 Sep 2019 - 11 Oct 2019

@ ICTP

Mathematics

School and Workshop on Gauge Theories and Differential Invariants | (smr 3326)

Address: Via Grignano, 9 I - 34151 Trieste (Italy)

Room: Kastler Lecture Hall (AGH)

Secretary: Monica Ancuta, Petra Krizmancic

Organizer(s): Giulio Bonelli (SISSA), Hiraku Nakajima (RIMS Kyoto, starting soon University of Tokyo, Kavli Institute for the Physics and Mathematics of the universe), Marcos Marino (University of Geneva), Alessandro Tanzini (SISSA), George Thompson (ICTP), Local Organiser: Lothar Goettsche

Cosponsor(s): Italian Institute for Nuclear Physics (INFN)infn

**DEADLINE: 15/06/2019**

ICTP - Strada Costiera, 11
I - 34151 Trieste Italy
(+39) 040 2240 111
pio@ictp.it

ICTP is governed by UNESCO, IAEA, and Italy, and is a UNESCO Category 1 Institute

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1st Latin American School in Applied Mathematics | (smr 3301)

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Trieste Algebraic Geometry Summer School (TAGSS) 2019 - Algebraic Geometry towards Applications | (smr 3306)

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EAUMP - ICTP Summer School on Algebraic Topology and its Applications | (smr 3310)

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Geometry , Mathematics , High Energy Cosmology and Astroparticle Physics

ICTP School on Geometry and Gravity | (smr 3311)

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School and Workshop on Mixing and Control | (smr 3324)

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Mathematics

School on Smooth and Homogeneous Dynamics | (smr 3271)

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School and Workshop on Random Matrix Theory and Point Processes | (smr 3382)

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School and Workshop on Gauge Theories and Differential Invariants | (smr 3326)

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Schools, conferences, workshops, and meetings

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1st Latin American School in Applied Mathematics | (smr 3301)

Activity

Mathematics

Trieste Algebraic Geometry Summer School (TAGSS) 2019 - Algebraic Geometry towards Applications | (smr 3306)

Activity

Mathematics

EAUMP - ICTP Summer School on Algebraic Topology and its Applications | (smr 3310)

Activity

Geometry , Mathematics , High Energy Cosmology and Astroparticle Physics

ICTP School on Geometry and Gravity | (smr 3311)

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Mathematics

School and Workshop on Mixing and Control | (smr 3324)

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Mathematics

School on Smooth and Homogeneous Dynamics | (smr 3271)

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School and Workshop on Random Matrix Theory and Point Processes | (smr 3382)

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School and Workshop on Gauge Theories and Differential Invariants | (smr 3326)

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