ICTP - Scientific Activities

Scientific Activities

Schools, conferences, workshops, and meetings

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Europe/Rome An ICTP Virtual Meeting The aim of the course is to provide training in the foundations of commutative algebra and algebraic geometry in prime characteristic and to present some of the exciting recent developments. The local theory of prime characteristic singularities is a beautiful and historically important subject. Singularities which are defined in terms of the behaviour of the Frobenius endomorphism have been labeled “F-singularities”. The course gives an introduction on the most prominent F-singularity classes that emerged from Hochster–Huneke’s tight closure theory. Since its introduction in the late 1980s, it has had a dramatic effect on the field of commutative algebra. Tight closure gives unified proofs and strong generalisations of many major theorems in commutative algebra, as well stimulated recent proofs of longstanding conjectures. Topics: An overview of tight closure of ideals Test ideals Direct summands F-rational rings and rational singularities Hilbert-Kunz multiplicities Briançon-Skoda Theorems Big Cohen-Macaulay algebras The absolute integral closure Symbolic powers of ideals The localisation problem Uniform Artin-Rees results Speakers: I. ABERBACH, University of Missouri, USA F. ENESCU, Georgia State University, USA N. EPSTEIN, George Mason University, USA E. GRIFO, University of Nebraska, USA G. LYUBEZNIK, University of Minnesota, USA L. MA, Purdue University, USA T. POLSTRA, University of Virginia, USA I. SWANSON, Purdue University, USA V. TRIVEDI, Tata Institute of Fundamental Research, India K. TUCKER, University of Illinois, USA W. ZHANG, University of Illinois, USA Schedule: Mondays and Wednesdays 1.00-3.00 pm GMT (link) Lectures. There will be 3 lectures and a tutorial on each topic each week. The speakers will provide detailed typed notes of their lectures on the day they finish their lectures. These notes will contain exercises which the participants should try to solve and submit to the tutorial instructor before 12 pm GMT on Fridays. Tutorials. The tutorial on each topic will be held a week after the lectures are delivered. The tutorial instructor will present solutions to problems assigned by the Lecturer that are received from the participants and discuss some material covered during the lectures. Grades will be assigned to the solutions. Registration: There is no registration fee. Online - ICTP pio@ictp.it

Activity

16 May 2022 - 25 Jul 2022

@ Online -

Mathematics

Graduate Course on Tight Closure of Ideals and its Applications | (smr 3707)

Room: Online

Secretary: Monica Petronela Ancuta, Viktoriya Lvova, Adriana Pinto

Organizer(s): K. MADDOX (University of Kansas, USA), K. GOEL (University of Utah, USA), M.E. ROSSI (University of Genoa, Italy), N. V. TRUNG (Institute of Mathematics, Vietnam), J. K. VERMA (Indian Institute of Technology Bombay, India), Local Organiser: Lothar Goettsche (ICTP)

Support E-Mail: smr3707@ictp.it

**DEADLINE: 31/03/2022**

Europe/Rome The AGRA series of summer schools (Santiago de Chile, 2012; Cusco, 2015; Córdoba, 2018; Online, 2021) has as its goal to foster the development of number theory in Latin America: it provides a formative experience for young researchers, and it also helps bring together more senior or mid-career mathematicians working in the field. It has been our tradition to have all courses and associated discussions in Spanish or Portuguese, in part so as to make all activities accessible to all students in Latin America, regardless of their English proficiency. The target audience of AGRA includes undergraduate students, graduate students and young researchers with a serious interest in number theory and neighboring fields. Due to the pandemic situation, AGRA IV was divided in two instalments. The first one was an ICTP – IMPA Online School that took place on August 16 – 20, 2021, with four minicourses covering topics in arithmetic combinatorics, arithmetic geometry, square-tiled surfaces and algebraic number theory (see http://indico.ictp.it/event/9617/). The plan for this second instalment, which shall happen in hybrid mode in the state of Rio de Janeiro – Brazil, is to have another group of minicourses, followed by tutorials and problem sessions. Minicourses will be as follows: Minicourse 1: Interactions between ergodic theory and number theory • Joel Moreira (Warwick, UK) • Sebastián Donoso (Univ. de Chile) Minicourse 2: Applications of homology and cohomology in group theory • Lev Glebsky (Universidad Autonoma de San Luis Potosi, Mexico) • Dessislava Kochloukova (Unicamp, Brazil) Minicourse 3: Expansion, divisibility and parity: a walk on numbers and graphs • Harald Helfgott (Univ. Göttingen, Germany/ CNRS, France) • Adrián Ubis (UAM, Spain) Minicourse 4: Arithmetic groups and homogenous dynamics • Sebastian Hurtado-Salazar (Univ. Chicago, USA) • Plinio Pino (UFF, Brazil) Minicourse 5: Mori dream surfaces • Michela Artebani (Univ. de Concepción, Chile) • Antonio Laface (Univ. de Concepción, Chile) Cabo Frio (Rio de Janeiro) - Brazil ICTP pio@ictp.it

Activity

20 Jun 2022 - 25 Jun 2022

@ Cabo Frio (Rio de Janeiro) - Brazil

Mathematics

AGRA IV (Arithmetic, Groups and Analysis) - Part 2 | (smr 3695)

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

Secretary: Doreen Sauleek

Organizer(s): Mikhail Belolipetsky (IMPA), Dimitar Dimitrov (UNESP), Harald Helfgott (Göttingen/CNRS), Matilde Lalín (Université de Montréal), Yuri Lima (Universidade Federal do Ceara), Suely Lima (IMPA), Roberto Miatello (Universidad Nacional de Córdoba), Ariel Pacetti (Universidade de Aveiro), Plinio Pino (UFF), Fernando Rodriguez-Villegas (ICTP), ICTP Scientific Contact: Emanuel Carneiro (ICTP)

Cosponsor(s): Instituto Serrapilheiraserra, Alexander von Humboldtavh, INCTMat inctmat, IMPAimpa, CNPqcnpq

**DEADLINE: 15/05/2022** Grants will be given to a selected number of participants. On-site participants should either have been fully vaccinated or recovered from COVID. **DEADLINE: 15/05/2022**

Europe/Rome An ICTP-EAUMP Hybrid Meeting. You can submit your application for participation in presence or online. This African Mathematical School is also an activity of AMU, supported by CIMPA Organised by the University of Nairobi, to be held at Kenya School of Government, Nairobi, Kenya The school will include: An intensive course in Programming in Python, coordinated by Jean-Baptiste Yunès (Institut de Recherche en Informatique Fondamentale, Université Paris Cité) where the participants will learn to write correct programs. An intensive course in Algorithms, coordinated by Roberto Mantaci (Institut de Recherche en Informatique Fondamentale, Université Paris Cité) where the participants will learn to write efficient programs. An intensive course on SageMath, a free, open-source, Python-based mathematics software system, coordinated by Anna Vanden Wyngaerd (Institut de Recherche en Informatique Fondamentale, Paris and Université libre de Bruxelles) where the participants will learn to apply to Mathematical Research the efficient programming techniques learnt in the two other courses. All courses will be composed of main lectures and applications in the form of exercise sessions or work sessions on machines. 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. Nairobi - Kenya ICTP pio@ictp.it

Activity

11 Jul 2022 - 29 Jul 2022

@ Nairobi - Kenya

Mathematics

ICTP-EAUMP School on Mathematical Programming and Algorithms - an African Mathematical School | (smr 3725)

Secretary: Monica Petronela Ancuta, Elizabeth Brancaccio, Viktoriya Lvova, Adriana Pinto

Organizer(s): Roberto MANTACI (Institut de Recherche en Informatique Fondamentale), Jared ONGARO (University of Nairobi), Balazs SZENDROI (University of Oxford), Paul VADERLIND (Stockholm University), Jean-Baptiste YUNES (Institut de Recherche en Informatique Fondamentale), ICTP Scientific Contact: Fernando Rodriguez Villegas (ICTP)

Cosponsor(s): Institut de Recherche en Informatique Fondamentaleirif1, CIMPAcimpa2, EAUMPeaump, Foundation Compositio Mathematicafcm, Uppsala Universityuppsala, African Mathematical Unionamu, University of Nairobiuon2

Support E-Mail: smr3725@ictp.it

**DEADLINE: 01/05/2022**

Activity

1 Aug 2022 - 5 Aug 2022

@ ICTP

Mathematics

Frontiers in Geometry and Topology Summer School | (smr 3648)

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

Secretary: Monica Ancuta, Viktoriya Lvova, Adriana Pinto

Organizer(s): Paul Feehan (Rutgers University), Lenny Ng (Duke University), Peter Ozsvath (Princeton University), Yongbin Ruan (Zhejiang University), Paul Seidel (MIT), Local Organiser: Claudio Arezzo

Cosponsor(s): Clay Mathematics Instituteclay1

Support E-Mail: smr3648@ictp.it

**DEADLINE: 28/02/2022**

Europe/Rome An ICTP Hybrid Meeting. You can submit your application for participation in presence or online. Organised in partnership with the Clay Mathematics Institute The conference is intended as an appreciation of the contributions of Tomasz Mrowka Geometry and Topology have seen spectacular recent developments, including the solution of classical problems. As a consequence, the established picture of how various parts of these areas fit together is evolving rapidly. On the topological side, among the topics that have progressed are: four-manifolds obtained as knot traces; knot concordance and homology cobordism, Stein fillings. On the Floer homology side, we have powerful new computational methods and new invariants of embedded graphs and webs. On the more analytic side, we have new compactness results and potential new invariants. Topics: Interplay of 3-dimensional and 4-dimensional Topology Floer homology theories and associated invariants Khovanov homology Geometric and analytic aspects of gauge theoretic equations Speakers: D. GABAI, Princeton University, USA L. GOETTSCHE, ICTP, Italy L. GUTH, MIT, USA J. HOM, Georgia Tech, USA C. HUGELMEYER, Princeton University, USA P. KRONHEIMER, Harvard University, USA F. LIN, Princeton University, USA R. LIPSHITZ, University of Oregon, USA P. LISCA, Università di Pisa, Italy C. MANOLESCU, Stanford University, USA G. MATIC, University of Georgia, USA R. MAZZEO, Stanford University, USA M. MILLER, Stanford University, USA E. MURPHY, Princeton University, USA J. PARDON, Princeton University, USA L. PICCIRILLO, MIT, USA J. PINZON CAICEDO, University of Notre Dame, USA J. RASMUSSEN, Cambridge, UK D. RUBERMAN, Brandeis University, USA A. STIPSICZ, Central European University, Hungary Z. SZABO, Princeton University, USA *C. TAUBES, Harvard University, USA D. WANG SUNY, Stony Brook, USA J. WANG, Harvard University, USA C. ZIBROWIUS, University of Regensburg, Germany *To be confirmed Here is the link to the Frontiers in Geometry and Topology Summer School Registration: 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. In person participation: As regards the COVID-19 policy, we advise to follow the updated rules available on the ICTP page Access Guidelines for Visitors. ICTP ICTP pio@ictp.it

Activity

8 Aug 2022 - 12 Aug 2022

@ ICTP

Mathematics

Frontiers in Geometry and Topology Research Conference | (smr 3649)

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

Secretary: Monica Ancuta, Viktoriya Lvova, Adriana Pinto

Cosponsor(s): Clay Mathematics Instituteclay1

Support E-Mail: smr3649@ictp.it

**DEADLINE: 28/02/2022**

Europe/Rome Vietnam Institute for Advanced Study in Mathematics (VIASM) https://viasm.edu.vn/en/hdkh/viasm-ictp-ss2022 The goal of this school is to introduce graduate students, advanced undergraduate students, young researchers, and interested mathematicians in Vietnam, Southeast Asia, and other countries in Asia, to basics of group representation theory, linear algebraic groups, structure and representation theory of finite groups of Lie type, including an introduction to the Deligne-Lusztig theory. It will also introduce the audience to a number of applications of group representation theory to various areas of mathematics, including number theory, algebraic geometry, and combinatorics. Hanoi - Viet Nam ICTP pio@ictp.it

Activity

9 Aug 2022 - 21 Aug 2022

@ Hanoi - Viet Nam

Mathematics

Summer School in Group Theory and Representation Theory | (smr 3730)

Secretary: Susanne Henningsen

Organizer(s): Le Minh Ha (Vietnam Institute for Advanced Study in Mathematics), Pham Huu Tiep (Rutgers University, USA ), ICTP Scientific Contact: Fernando Rodriguez Villegas (ICTP)

Cosponsor(s): Vietnam Institute for Advanced Study in Mathematicsviasm2

**DEADLINE: 30/05/2022**

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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Scientific Activities

Schools, conferences, workshops, and meetings

Activity

Mathematics

Graduate Course on Tight Closure of Ideals and its Applications | (smr 3707)

Activity

Mathematics

AGRA IV (Arithmetic, Groups and Analysis) - Part 2 | (smr 3695)

Activity

Mathematics

ICTP-EAUMP School on Mathematical Programming and Algorithms - an African Mathematical School | (smr 3725)

Activity

Mathematics

Frontiers in Geometry and Topology Summer School | (smr 3648)

Activity

Mathematics

Frontiers in Geometry and Topology Research Conference | (smr 3649)

Activity

Mathematics

Summer School in Group Theory and Representation Theory | (smr 3730)

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Scientific Activities

Schools, conferences, workshops, and meetings

Activity

Mathematics

Graduate Course on Tight Closure of Ideals and its Applications | (smr 3707)

Activity

Mathematics

AGRA IV (Arithmetic, Groups and Analysis) - Part 2 | (smr 3695)

Activity

Mathematics

ICTP-EAUMP School on Mathematical Programming and Algorithms - an African Mathematical School | (smr 3725)

Activity

Mathematics

Frontiers in Geometry and Topology Summer School | (smr 3648)

Activity

Mathematics

Frontiers in Geometry and Topology Research Conference | (smr 3649)

Activity

Mathematics

Summer School in Group Theory and Representation Theory | (smr 3730)

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