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Description
Workshop web page is at THIS LINK.

The school will introduce commutative algebra and algebraic geometry in prime characteristics and their relationship with complex algebraic geometry. There have been many important developments in these fields during the last three decades.  There will be four courses of lectures to highlight some of these developments related to vector bundles and tight closure, singularities in prime characteristics, F-signature and Hilbert-Kunz multiplicity and study of singularities via Big Cohen-Macaulay (BCM)-algebras, perfectoid spaces and Frobenius splitting.

Topics:
  • Vector bundles and tight closure
  • Singularity invariants in positive characteristic
  • Singularities via BCM Algebras
  • F-singularities — applications of characteristic p methods to singularity theory

Confirmed Speakers:
Holger BRENNER, University of Osnabrueck, Germany
Ilya SMIRNOV, Basque Centre for Applied Mathematics, Spain
Kevin TUCKER, University of Illinois at Chicago, USA
Keiichi WATANABE, Nihon University, Tokyo, Japan
 
Applicants are encouraged to submit an abstract to give a contributed talk. During the application please make sure to use our templates to format your abstract. Templates are available below for download.

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.
 

Material

School on Commutative Algebra and Algebraic Geometry in Prime Characteristics | (smr 3866)
Go to day
  • Tuesday, 2 May 2023
    • 08:30 - 09:00 Registration formalities 
      REGISTRATION: Upon arrival, Visitors not staying in the ICTP Guest Houses, are kindly requested to complete registration formalities at the Leonardo Building (Lobby). The Registration Desk will be open from 8.30 to 9.00.
    • 09:00 - 18:50 
      Morning session Chair: L.T. HOA, Institute of Mathematics, Vietnam
Afternoon session Chair: P.H. QUY, FPT University, Vietnam
      • 09:00 Vector bundles and tight closure 50'
        Speaker: H. BRENNER (University of Osnabrueck, Germany)
        Material: Abstract Video
      • 10:00 F-singularities — applications of characteristic p methods to singularity theory 50'
        Speaker: K. WATANABE (Nihon University, Tokyo, Japan)
        Material: Abstract Slides Video
      • 11:00 Coffee break 30'
      • 11:30 Polynomial invariant rings in modular invariant theory 15'
        Speaker: M. MONDAL (IIT Jodhpur, India)
        Material: Slides Video
      • 11:50 Local cohomology of invariant rings 15'
        Speaker: K. GOEL (Basque Centre for Applied Mathematics, Spain)
        Material: Slides Video
      • 12:10 Groebner deformations and F-singularities 15'
        Speaker: M. KOLEY (ISI, Kolkata, India)
        Material: Slides Video
      • 12:30 Lunch break 1h30'
      • 14:00 Singularity invariants in positive characteristic 50'
        Speaker: I. SMIRNOV (Basque Centre for Applied Mathematics, Bilbao, Spain)
        Material: Abstract Video
      • 15:00 Singularities via BCM Algebras 50'
        Speaker: K. TUCKER (University of Illinois at Chicago, IL, USA)
        Material: Abstract Slides Video
      • 16:00 Coffee break 30'
      • 16:30 The Frobenius test exponents in prime characteristic 15'
        Speaker: D. HUONG (Thang Long University, Vietnam)
        Material: Slides Video
      • 16:50 F-threshold of filtration of ideals 15'
        Speaker: A. KUMAR (Chennai Mathematical Institute, India)
        Material: Slides Video
      • 17:10 The F-rationality of Blow-up 15'
        Speaker: N. KOTAL (Chennai Mathematical Institute, India)
        Material: Video
      • 17:30 Welcome reception 1h0'
  • Wednesday, 3 May 2023
    • 09:00 - 17:30 
      Morning session Chair: V. TRIVEDI, Tata Institute of Fundamental Research, India
Afternoon session Chair: M. MANDAL, Indian Institute of Technology Kharagpur, India
      • 09:00 Vector bundles and tight closure 50'
        Speaker: H. BRENNER (University of Osnabrueck, Germany)
        Material: Abstract Video
      • 10:00 F-singularities — applications of characteristic p methods to singularity theory 50'
        Speaker: K. WATANABE (Nihon University, Tokyo, Japan)
        Material: Abstract Video
      • 11:00 Group photo & Coffee break 30'
      • 11:30 Perturbations of ideals in local rings 15'
        Speaker: L. DUARTE (University of Genoa, Italy)
        Material: Video
      • 11:50 Epsilon multiplicity in graded dimension two and density functions 15'
        Speaker: S. DAS (IIT Bombay, India)
        Material: Poster Slides Video
      • 12:10 A density function for a Noetherian filtration of homogeneous ideals 15'
        Speaker: S. ROY (TIFR, Mumbai, India)
        Material: Poster Slides Video
      • 12:30 Lunch break 1h30'
      • 14:00 Singularity invariants in positive characteristic 50'
        Speaker: I. SMIRNOV (Basque Centre for Applied Mathematics, Bilbao, Spain)
        Material: Abstract Video
      • 15:00 Singularities via BCM Algebras 50'
        Speaker: K. TUCKER (University of Illinois at Chicago, IL, USA)
        Material: Abstract Slides Video
      • 16:00 Coffee break 30'
      • 16:30 The Weak Lefschetz Property of monomial ideals and Mixed Multiplicities of ideals 15'
        Speaker: H. THIAGO (Dalhousie University, Canada)
        Material: Video
      • 16:50 The Hilbert functions of Artinian local complete intersections 15'
        Speaker: S. MASUTI (IIT Dharwad, India)
        Material: Slides Video
      • 17:10 Bounds for the reduction number of primary ideals in dimension three 15'
        Speaker: S. KUMARI (IIT Patna, India)
        Material: Slides Video
  • Thursday, 4 May 2023
    • 09:00 - 17:30 
      Morning session Chair: C. D’CRUZ, Chennai Mathematical Institute, India
Afternoon session Chair: A.A. QURESHI, Sabanci University, Turkey
      • 09:00 Vector bundles and tight closure 50'
        Speaker: H. BRENNER (University of Osnabrueck, Germany)
        Material: Abstract Video
      • 10:00 F-singularities — applications of characteristic p methods to singularity theory 50'
        Speaker: K. WATANABE (Nihon University, Tokyo, Japan)
        Material: Abstract Video
      • 11:00 Coffee break 30'
      • 11:30 (Non) linearity of regularity of Tor over complete intersections in positive characteristic 15'
        Speaker: D. GHOSH (IIT Kharagpur, India)
        Material: Slides Video
      • 11:50 Betti cones over fiber products 15'
        Speaker: O. JAVADEKAR (IIT Bombay, India)
        Material: Video
      • 12:10 On regularity of symbolic and ordinary powers of weighted oriented graphs 15'
        Speaker: M. KUMAR (IIT Kharagpur, India)
        Material: Slides Video
      • 12:30 Lunch break 1h30'
      • 14:00 Singularity invariants in positive characteristic 50'
        Speaker: I. SMIRNOV (Basque Centre for Applied Mathematics, Bilbao, Spain)
        Material: Abstract Video
      • 15:00 Singularities via BCM Algebras 50'
        Speaker: K. TUCKER (University of Illinois at Chicago, IL, USA)
        Material: Abstract Slides Video
      • 16:00 Coffee break 30'
      • 16:30 Symbolic powers of edge ideals of weighted oriented graphs 15'
        Speaker: M. MANDAL (IIT Kharagpur, India)
        Material: Slides Video
      • 16:50 Invariants of binomial edge ideals via linear programs 15'
        Speaker: A. LACLAIR (Purdue University, USA)
        Material: Video
      • 17:10 Tight Hilbert polynomial and F-rational local rings 15'
        Speaker: S. DUBEY (IIT Bombay, India)
        Material: Slides Video
  • Friday, 5 May 2023
    • 09:00 - 17:25 
      Morning session Chair: V. MUKUNDAN, IIT Delhi, India
Afternoon session Chair: J. VERMA, IIT Bombay Mumbai, India
      • 09:00 Vector bundles and tight closure 50'
        Speaker: H. BRENNER (University of Osnabrueck, Germany)
        Material: Abstract Video
      • 10:00 F-singularities — applications of characteristic p methods to singularity theory 50'
        Speaker: K. WATANABE (Nihon University, Tokyo, Japan)
        Material: Abstract Video
      • 11:00 Coffee break 30'
      • 11:30 Affine semigroups of maximal projective dimension 15'
        Speaker: O.P. BHARDWAJ (IIT Gandhinagar, India)
        Material: Slides Video
      • 11:50 The v-Number of Monomial Ideals 15'
        Speaker: K. SAHA (IIT Gandhinagar, India)
        Material: Video
      • 12:10 Betti sequence of the projective closure of affine monomial curve 15'
        Speaker: P. SRIVASTAVA (IIT Gandhinagar, India)
        Material: Video
      • 12:30 Lunch break 1h30'
      • 14:00 Singularity invariants in positive characteristic 50'
        Speaker: I. SMIRNOV (Basque Centre for Applied Mathematics, Bilbao, Spain)
        Material: Abstract Video
      • 15:00 Singularities via BCM Algebras 50'
        Speaker: K. TUCKER (University of Illinois at Chicago, IL, USA)
        Material: Abstract Slides Video
      • 16:00 Coffee break 30'
      • 16:30 Image of linear derivations and Mathieu-Zhao subspaces 15'
        Speaker: S. GUPTA (IIT Delhi, India)
        Material: Slides Video
      • 16:50 (A,d)-modules, Hochschild homology and higher derivations 15'
        Speaker: S. KOUR (IIT Delhi, India)
        Material: Video
      • 17:10 Upper bounds on two Hilbert coefficients 15'
        Speaker: X.D. LE (Hong Duc University, Vietnam)
        Material: Slides Video
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