Curriculum Vitae

Paolo Cascini

Department of Mathematics Tel. (818) 294-5315 University of California at Santa Barbara Fax. (805) 893-2385 Santa Barbara, CA 93106 cascini@math.ucsb.edu

Personal Data

• Citizenship - Italian.

• Current Status - U.S. Permanent Resident.

Research Interests

• Algebraic Geometry - Birational Geometry, Minimal Model Program.

• Several Complex Variables - Kähler Manifolds.

Education

• Universitá di Firenze – Firenze, Italy Mathematics, B.S. (1998), M.S. (2000).

• Courant Institute of Mathematical Sciences, New York University – New York, NY Mathematics, M.S. (2002), Ph.D. (2004) (Advisor: Prof. F.A. Bogomolov).

Appointments

• 2007– present; University of California at Santa Barbara - Assistant Professor.

• 2004 – 07; University of California at Santa Barbara - Visiting Assistant Professor.

Awards

• A.P. Sloan Fellowship, 2008.

• Wilhelm T. Magnus Prize for Significant Contributions to Mathematical Sciences Courant Institute, New York University, 2005.

• Awarded 5-year McCracken Fellowship Program to pursue Ph.D. in Mathematics (2000-2004) at New York University.

Selected Publications

• (with C. Birkar, C. Hacon, J. M^{c} Kernan) Existence of Minimal Models for Varieties of Log General Type, math.AG/0610203.

• (with M. Nakamaye) Seshadri Constants on Smooth Three–folds, Submitted.

• (with G. La Nave) Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties, Submitted.

• Subsheaves of the Cotangent Bundle, Central European Journal of Math. 4 (2006), no. 2, 209–224.

• (with F.A. Bogomolov and B. de Oliveira) Singularities on Complete Algebraic Varieties, Central European Journal of Math. 4 (2006), no. 2, 194–208.

• On the moduli space of the Schwarzenberger bundles, Pacific J. Math. 205 (2002), no. 2, 311–323.

• Weighted Tango Bundles on ℙ^{n} and their moduli spaces, Forum Math. 13 (2001), no. 2, 251–260.

Invited Talks

• Harvard/MIT Algebraic Geometry Seminar, MIT, May 6, 2008 Title: "On the Minimal Model Program".

• Algebraic Geometry Seminar, University of Michigan, Apr. 16, 2008 Title: "On the Minimal Model Program".

• AMS Meeting, Bloomington, Apr. 6, 2008 Title: “On the Minimal Model Program”.

• Algebraic Geometry Seminar, University of Chicago, Mar. 12, 2008 Title: “On the Minimal Model Program”.

• AMS Meeting, Albuquerque, Oct. 13, 2007 Title: “On the Minimal Model Program”.

• Mini-Course in Algebraic Geometry, National Tsing Hua University, July 3-7, 2007 Title: “Finite Generation of the Canonical Ring I, II, III & IV”.

• Algebraic Geometry Seminar, University of Massachusetts, May 6, 2007 Title: “Finite Generation of the Canonical Ring”.

• Colloquium, University of Massachusetts, May 5, 2007 Title: “On the Minimal Model Program”.

• Colloquium, Yeshiva University, Feb. 27, 2007 Title: “On the Minimal Model Program”.

• Colloquium, Stony Brook University, Feb. 26, 2007 Title: “On the Minimal Model Program”.

• Southern California Algebraic Geometry Seminar, San Diego, Feb. 24, 2007 Title: “Finite Generation of the Canonical Ring”.

• Colloquium, Northwestern University, Feb. 16, 2007 Title: “On the Minimal Model Program”.

• Gadget Seminar, U.T. Austin, Jan. 30, 2007 Title: “On the Minimal Model Program”.

• Algebraic Geometry Seminar, Johns Hopkins University, Jan. 24, 2007 Title: “On the Minimal Model Program (part II)”.

• Colloquium, Johns Hopkins University, Jan. 23, 2007 Title: “On the Minimal Model Program”.

• Colloquium, U.C. Santa Barbara, Jan. 22, 2007 Title: “On the Minimal Model Program”.

• Colloquium, University of Western Ontario, Jan. 19, 2007 Title: “On the Minimal Model Program”.

• Colloquium, Vanderbilt University, Jan. 16, 2007 Title: “On the Minimal Model Program”.

• Colloquium, Cambridge University, Jan. 10, 2007 Title: “On the Minimal Model Program”.

• Algebraic Geometry Seminar, Universitá di Firenze, Dec. 20, 2006 Title: “On the Minimal Model Program”.

• Western Algebraic Geometry Seminar, Salt Lake City, Nov. 11, 2006 Title: “Minimal Model Program for Varieties of General Type”.

• Recent trends in higher dimensional geometry, BIRS, Banff, April 2, 2006 Title: "Kähler-Ricci Flow and the Minimal Model Program on a Projective Variety".

• Algebraic Geometry Seminar, University of Michigan, Feb. 22, 2006 Title: "Kähler-Ricci Flow and the Minimal Model Program on a Projective Variety".

• Colloquium, University of Alberta, Mar. 24, 2005 Title: "Kähler-Ricci Flow and the Minimal Model Program on a Projective Variety".

• Algebra, Geometry and Physics Seminar at Stony Brook, April 14, 2004 Title: "On the Subsheaves of the Cotangent Bundle".

• Giornate di Geometria Algebrica ed Argomenti Correlati VI, Anacapri, May 31, 2002 Title: "On the Subsheaves of the Cotangent Bundle and its Exterior Powers".

• Geometrie Algebrique en Liberte", Luminy, March 29, 2000 Title: "On the Moduli Space of Rational Normal Curves".

• Geometric Properties of Real and Complex Varieties, Palermo, Aug. 30, 1999 Title: "Weighted Tango Bundles".

Seminar Talks

• Graduate Colloquium, Oct. 11, 2007 Title: “On the Minimal Model Program”.

• Geometry, Topology, and Physics Seminar, May 25, 2007 Title: “On the Kähler-Ricci Flow”.

• Seminar of Geometry and Arithmetic, Feb. 24, 2006 Title: “Kähler-Ricci Flow and the Minimal Model Program for Projective Varieties”.

• Talks on Derived Categories, Jan. 27, 2006 Title: “ Log Crepant Birational Maps and Derived Categories”.

• Talks on Derived Categories, Oct. 7, 2005 Title: “ An introduction to Fourier-Mukai Transforms”.

• Seminar of Differential Geometry, Apr. 1, 2005 Title: "Kähler-Ricci Flow and the Minimal Model Program on a Projective Variety".

• Seminar of Geometry and Arithmetic, Nov. 29, 2004 Title: "3-fold flips after Shokurov, II".

• Seminar of Geometry and Arithmetic, Nov. 25, 2004 Title: "3-fold flips after Shokurov, I".

• Seminar of Geometry and Arithmetic, Oct. 14, 2004 Title: "Singularities in the Minimal Model Program".

• Seminar of Geometry and Arithmetic, Sep. 23, 2004 Title: "On the Stability of the Cotangent Bundle of a Projective Variety".

Teaching Experience

• University of California, Santa Barbara Winter 2008 - Lectured an undergraduate class in Calculus I. Fall 2007 - Lectured an undergraduate class in Topology. Spring 2007 - Lectured an undergraduate class in Calculus II. Winter 2007 - Lectured two undergraduate classes in Calculus I & II. Fall 2006 - Lectured an undergraduate class in Vector Calculus II. Spring 2006 - Lectured an undergraduate class in Vector Calculus I. Winter 2006 - Lectured two undergraduate classes in Calculus I and ODE.

Fall 2005 - Lectured an undergraduate class in Calculus I. Spring 2005 - Lectured an undergraduate class in Calculus II. Winter 2005 - Lectured an undergraduate class in Calculus I. Fall 2004 - Lectured two undergraduate classes in Calculus I & II.

• New York University Spring 2004 - Taught a graduate recitation class in PDE. Fall 2003 - Lectured an undergraduate class in Calculus I. Summer 2003 - Lectured an undergraduate class in Linear Algebra. Spring 2003 - Taught a graduate recitation class in PDE. Fall 2002 - Taught a recitation section in Algebra. Fall 2001 - Taught a recitation section in Business Calculus. Spring 2001 - Taught recitation section in Vector Analysis.