LAURA GHEZZI

 Education                   

 

Ph.D. in Mathematics, August 2001

Michigan State University, East Lansing, MI.

Thesis Advisor: Prof. B. Ulrich.

Thesis: The depth of blow-up rings of ideals.

 

 B.S. (Laurea) in Mathematics, February 1995 

Università degli Studi di Genova, Italy. 

Thesis Advisor: Prof. G. Valla.

Thesis: Risoluzioni minimali di schemi zero dimensionali ridotti.

 

Positions Held                       

 

            2012 –             Associate Professor at the New York City College of Technology.

            2007 – 2012    Assistant Professor (tenure track) at the New York City College of Technology.

2004 – 2007    Assistant Professor (tenure track) at Florida International University.

2001 – 2004    Post Doctoral Fellow at the University of Missouri-Columbia.

1995 – 2001    Teaching Assistant at Michigan State University.

 

Research Interests    

 

Primary: Commutative Algebra.

Secondary: Algebraic Geometry, Computational Algebra, and Homological Algebra.

 

Publications    

 

·        The Chern numbers and Euler characteristics of modules  (with S. Goto, J. Hong, K. Ozeki, T.T. Phuong and W.V. Vasconcelos), preprint.


·        Variation of Hilbert coefficients  (with S. Goto, J. Hong and W.V. Vasconcelos), Proceedings of the American Mathematical Society 141 (2013), 3037-3048.


·         Variation of the first Hilbert coefficients of parameters with a common integral closure  (with S. Goto, J. Hong, K. Ozeki, T.T. Phuong and W.V. Vasconcelos), Journal of Pure Appl. Algebra 216 (2012), 216-232.

 

·         Cohen-Macaulayness versus the vanishing of the first Hilbert coefficient of parameter ideals  (with S. Goto, J. Hong, K. Ozeki, T.T. Phuong and W.V. Vasconcelos), J. London Math. Society 81 (2010), 679-695.

 

·        A generalization of the Strong Castelnuovo Lemma, J. Algebra 323 (2010), 1018-1035.

 

·         The signature of the Chern coefficients of local rings (with J. Hong and W.V. Vasconcelos), Math. Research Letters 16 (2009), 279-289.

 

·         Toroidalization of generating sequences in dimension two function fields of positive characteristic (with O. Kashcheyeva),  J. Pure Appl. Algebra 209 (2007), 631-649.

 

·         Toroidalization of generating sequences in dimension two function fields (with H. T. Hà and O. Kashcheyeva), J. Algebra 301 (2006), 838-866.

 

·         Homology multipliers and the relation type of parameter ideals (with I. Aberbach and H. T Hà), Pacific J. Math. 226 (2006), 1-39.

 

·         Completions of valuation rings (with S.D. Cutkosky), Recent progress in arithmetic and algebraic geometry, Contemp. Math. 386, 13-34, Amer. Math. Soc., Providence, RI, 2005.

 

·         The depth of the associated graded ring of ideals with any reduction number (with I. Aberbach and H. T. Hà), J. Algebra 276 (2004), 168-179.

 

·         Cohen-Macaulayness of special fiber rings (with A. Corso, C. Polini and B. Ulrich), Comm. Algebra 31 (special issue in honor of S. Kleiman) (2003), 3713-3734.

 

·         On the depth of the associated graded ring of an ideal, J. Algebra 248 (2002), 688-707.

 

Other Publications    

 

·         Negativity Conjecture for the first Hilbert coefficient (with S. Goto, J. Hong, K. Ozeki, T.T. Phuong and W.V. Vasconcelos), arXiv:1005.0105 [math.AC].

 

·         A generalization of the Strong Castelnuovo Lemma for n+4 points in the n-dimensional projective space, Proceedings of the 2008 School of Arts and Sciences Annual Research Conference, New York City College of Technology, Linus Publications, 9-13.

 

·         The depth of blow-up rings of ideals, Michigan State University, Ph.D. Thesis.

 

Professional Activities

  

Co-founder and co-organizer of the Commutative Algebra and Algebraic Geometry Seminar at the CUNY Graduate Center, since 2008.


Co-organizer of the Eighth Colloquiumfest at the CUNY Graduate Center (March 6-7, 2009).

 

Member of the Organizing Committee of the City Tech Research Conference and of the City Tech Student Research Conference (March 28, 2008, March 27, 2009, May 8, 2009, April 1, 2011, May 5, 2011, March 30, 2012, May 10, 2012, April 5, 2013).

 

Co-organizer (with H. T. Hà and A. Simis) of the Special Session Commutative Algebra and Algebraic Geometry at the AMS Spring Southeastern Sectional Meeting at Florida International University, Miami, FL (April 1-2, 2006).

 

Referee for the Journal of Pure and Applied Algebra, Communications in Algebra, Journal of Algebra, Proceedings of the American Mathematical Society, Bulletin of the London Mathematical Society, Proceedings of the Second International Conference and Workshop on Valuation Theory, American Mathematical Monthly, Journal of the Mathematical Society of Japan.

 

Awards and Fellowships

 

            PSC-CUNY Research Award, 2008-2009, 2009-2010, 2010-2011, 2013-2014.


            Office of the Provost / FIU Foundation Faculty Research Award, Summer 2006.

           

            Travel Support to attend the Fields Institute Summer School and Conference “Valuations and

             Integral Closures in Commutative Algebra”, University of Ottawa, Ottawa, Canada, July 3-22,

             2006.

 

AWM Travel Grant in connection with the First International Meeting between the American Mathematical Society and Various Indian Mathematical Societies, Bangalore, India, December 17-20, 2003.


Travel Support in connection with the 2003 AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Presentations by Young Researchers, Snowbird, Utah, July 20-24, 2003.


General Member at MSRI (Berkeley) for the program Commutative Algebra, November 2002.


Graham Fellowship, Department of Mathematics, Michigan State University, Summer 2001

and Summer 1999.


Dissertation Completion Fellowship, Department of Mathematics, Michigan State University,

Spring 2001.


Laurea, Summa cum Laude, Università degli Studi di Genova, Italy, 1995.

 

 

 Talks

  1.  The first Hilbert coefficients, Union College Mathematics Conference, Schenectady, NY (October 19-20, 2013).

  2. Variation of the first Hilbert coefficient, Workshop on Representation Theory, Homological Algebra, and Free Resolutions, MSRI, Berkeley (February 11-17, 2013).

  3. Hilbert coefficients of parameter ideals relative to a module, American Mathematical Society Meeting, Tulane University, New Orleans, LA (October 13-14, 2012).

  4. The first Hilbert coefficient of parameter ideals, School and Workshop on Local Rings and Local Study of Algebraic Varieties, ICTP (International Centre for Theoretical Physics), Trieste, Italy (June 7-11, 2010).

  5. Cohen-Macaulayness and the vanishing of Hilbert coefficients, American Mathematical Society Sectional Meeting, Pennsylvania State University, PA (October 24-25, 2009).

  6. A generalization of the Strong Castelnuovo Lemma, Winter Meeting of the Canadian Mathematical Society, Ottawa, Canada (December 6-8, 2008).

  7.  A generalization of the Strong Castelnuovo Lemma, International Conference on Commutative Algebra “Towards Establishing a Cutting-Edge Platform for Commutative Ring Theory in the 21th Century”, Yokohama, Japan (March 17-21, 2008).

  8.  A generalization of the Strong Castelnuovo Lemma, Rutgers University (February 2008).

  9. Blow-ups in monomialization problems, American Mathematical Society Sectional Meeting, Rutgers University, NJ (October 6-7, 2007).

  10. Monomialization of generating sequences of valuations in two dimensional function fields, Fields Institute Summer School and Conference “Valuations and Integral Closures in Commutative Algebra”, University of Ottawa, Ottawa, Canada (July 3-22, 2006).

  11. Generating sequences of valuations, Florida Atlantic University (February 2006).

  12. Monomialization of generating sequences of valuations, CIMPA School on Commutative Algebra, Institute of Mathematics of the Vietnamese Academy of Science and Technology, Hanoi, Vietnam (January 3-7, 2006).

  13. Generating sequences of valuations, University of Missouri-Columbia (May 2005).

  14. Valuations in Algebraic Geometry, Colloquium, Tulane University (February 2005).

  15. Homology multipliers and the relation type of parameter ideals, American Mathematical Society Sectional Meeting, Nashville, TN (October 16-17, 2004).

  16. An introduction to valuations, Florida Atlantic University (August 2004).

  17. Homology multipliers and the relation type of parameter ideals, School on Commutative Algebra and its Interactions with Algebraic Geometry and Combinatorics, ICTP (International Centre for Theoretical Physics), Trieste, Italy (June 7-11, 2004).

  18. Rank one valuations, University of Genova, Italy (June 2004).

  19. Valutazioni in Geometria Algebrica, Giornate di Geometria Algebrica ed argomenti correlati VII, Rimini, Italy (May 18-22, 2004).

  20. Bounding the relation type of parameter ideals, American Mathematical Society Sectional Meeting, Tallahassee, FL (March 12-13, 2004).

  21. Valuations in Algebraic Geometry, Colloquium, University of Montana (February 2004).

  22. Valuations in Algebraic Geometry, Colloquium, University of Maine (February 2004).

  23. Valuations in Algebraic Geometry, Colloquium, Florida International University (January 2004).

  24. Valuations in Algebraic Geometry, Colloquium, Loyola College in Maryland (January 2004).

  25. The role of valuation theory in Algebraic Geometry: Local uniformization theorems, American Mathematical Society Annual Meeting, Phoenix, AZ (January 7-10, 2004).

  26. Valuations in Algebraic Geometry, The 14th International Conference of the Jangjeon Mathematical Society, Mysore, India (December 22-24, 2003).

  27. Completions of rank one valuation rings, First International Meeting between the American Mathematical Society and Various Indian Mathematical Societies, Bangalore, India (December 17-20, 2003).

  28. When is the "union of the completions" a valuation ring?, University of Nebraska at Lincoln (November 2003).

  29. A local uniformization theorem for rank one valuations, Route 81 Conference on Commutative Algebra and Algebraic Geometry, Syracuse University (October 4, 2003).

  30. Completions of valuation rings, KUMUNU: 5th Algebra Day, University of Kansas (September 13, 2003).

  31. Completions of relative local uniformization, 2003 AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Presentations by Young Researchers, Snowbird, Utah (July 20-24, 2003).

  32. Completions of rank one valuation rings, University of Genova, Italy (July 2003).

  33. Valuations and blow-ups, Michigan State University (January 2003).

  34. The depth of the associated graded ring of ideals with any reduction number, Current Trends in Commutative Algebra, Centro Internazionale di Ricerca Matematica, Levico, Italy (June 16-21, 2002).

  35. The depth of blow-up rings of ideals, American Mathematical Society Sectional Meeting, Montreal (May 3-5, 2002).

  36. The depth of the associated graded ring of an ideal, First Joint International Meeting between the American Mathematical Society and the Sociètè Mathèmatique de France, Lyon, France (July 17-20, 2001).

 

Talks and Conferences at CUNY


  1. Variation of Hilbert coefficients, City Tech Eleventh Annual Poster Session for Faculty and Student Research (November 21, 2013).

  2. Variation of the first Hilbert coefficients of parameter ideals with a common integral closure, Commutative Algebra and Algebraic Geometry Seminar, CUNY Graduate Center (September 20, 2013).

  3. Hilbert coefficients of parameter ideals with a common integral closure, City Tech Tenth Annual Poster Session for Faculty and Student Research (November 15, 2012).

  4. Hilbert polynomials in local rings, Forward to Professorship Poster Session, New York City College of Technology (March 3, 2012).

  5. Conjectures on Hilbert polynomials in local rings, City Tech Ninth Annual Poster Session for Faculty and Student Research (November 17, 2011).

  6. The first Hilbert coefficients of parameter ideals relative to a module, Commutative Algebra and Algebraic Geometry Seminar, CUNY Graduate Center (February 2011).

  7. A generalization of the Strong Castelnuovo Lemma, City Tech Eighth Annual Poster Session for Faculty and Student Research (November 18, 2010).

  8. Linear syzygies in minimal free resolutions of algebraic varieties, New York Algebra Colloquium, CUNY Graduate Center (October 8, 2010).

  9. Hilbert coefficients in local rings, City Tech Seventh Annual Poster Session for Faculty and Student Research (November 19, 2009).

  10. Minimal free resolutions in Commutative Algebra, and applications to Computational Algebra, C-LAC (Center for Logic, Algebra and Computation), New York City College of Technology, November 2009.

  11. A proof of the conjecture on the vanishing of the first Hilbert coefficient of parameter ideals, Commutative Algebra and Algebraic Geometry Seminar, CUNY Graduate Center (October 2009).

  12. Hilbert functions in local rings, Commutative Algebra and Algebraic Geometry Seminar, CUNY Graduate Center (September 2009).

  13. Summer Institute for Teaching and Learning and Learning Communities Planning, New York City College of Technology (May 26-29, 2009).

  14. Minimal free resolutions of points, City Tech Sixth Annual Poster Session for Faculty and Student Research (November 13, 2008).

  15. Valuations, Singularities and Blow-ups, Colloquium, New York City College of Technology (November 6, 2008).

  16. NYSMATYC Regional Conference, New York City College of Technology (October 19, 2008).

  17. Minimal free resolutions of points in the projective space, Commutative Algebra and Algebraic Geometry Seminar, CUNY Graduate Center (September 2008).

  18. Second NYWIMN Conference (New York Women in Mathematics Network), New York City College of Technology (May 2, 2008).

  19. Generalizations of the Strong Castelnuovo Lemma, City Tech Research Conference (March 28, 2008).

  20. Valuations in Algebraic Geometry, City Tech Fifth Annual Poster Session for Faculty and Student Research (November 15, 2007).

  21. Valuations in Algebraic Geometry, City Tech Math Seminar Series (October 2007).

  22. Summer Institute for Teaching and Learning, New York City College of Technology (May 29-31, 2007).

 

Students Mentored

 

  1. Parveen Chowdhury, under the Emerging Scholars Program at the New York City College of Technology, in connection with the Second NYWIMN Conference, Spring 2008.

 

 

Other Conferences

 

  1. Commutative Algebra and its Interactions, in honor of Mel Hochster, Ann Arbor, MI (July 31-August 5, 2008).

  2. Hilbert Functions and Syzygies in Commutative Algebra and Combinatorics, in honor of Juergen Herzog, Cortona, Italy (September 17-21, 2007).

  3. MAGIC 05 (Midwest Algebra, Geometry and their Interactions Conference), University of Notre Dame, Notre Dame, IN (October 7-11, 2005).

  4. Workshop on resolution of singularities, factorization of birational mappings, and toroidal geometry, BIRS (Banff International Research Station), Banff, Canada (December 11-16, 2004).

  5. Lisbon Conference on Commutative Algebra, Lisbon, Portugal (June 23-27, 2003).

  6. Workshop on ``Commutative Algebra: Local and Birational Theory'', MSRI, Berkeley, CA (December 2-6, 2002).

  7. KUMUNU: 4th Algebra Day, University of Kansas (September 28, 2002).

  8. Commutative Algebra: Hilbert functions, homological methods, and combinatorial aspects, 1st Joint International Meeting of the American Mathematical Society and the Unione Matematica Italiana, Pisa, Italy (June 12-16, 2002).

  9. Commutative Algebra Days, University of Nebraska at Lincoln (March 15-16, 2002).

  10. KUMUNU: 3rd Algebra Day, University of Kansas (September 29, 2001).

  11. American Mathematical Society Sectional Meeting, Lawrence, KS (March 30-31, 2001).

  12. American Mathematical Society Sectional Meeting, Notre Dame, IN (April 7-9, 2000).

  13. American Mathematical Society Annual Meeting, Washington, D.C. (January 19-22, 2000).

  14. Homological Methods in Commutative Algebra and Algebraic Geometry, Genova, Italy (June 1-8, 1998).

  15. Midwest Algebraic Geometry Conference, University of Notre Dame, Notre Dame,  IN (November 7-9, 1997).

  16. American Mathematical Society Sectional Meeting, Kent, OH (November 3-4, 1995).

  17. COCOA IV (COmputational COmmutative Algebra), Genova, Italy (May 29-June 2, 1995).

  18. Workshop in Commutative Algebra, Genova, Italy (March 29-31, 1995).

  19. Workshop on Commutative Algebra and its Relation to Combinatorics and Computer Algebra, ICTP (International Centre for Theoretical Physics), Trieste, Italy (May 16-27, 1994).

 

 

 Teaching Experience

 

Assistant/Associate Professor at the New York City College of Technology, 2007- Present

 

  MAT 1175 Fundamentals of Mathematics (regular class and Learning Communities),

  MAT 1275 College Algebra and Trigonometry,

  MAT 1375 Precalculus,

  MAT 1475 Calculus I,

  MAT 1575 Calculus II,

  MAT 2440 Discrete Structures and Algorithms I.

  MAT 2675 Calculus III

  MAT 2580 Introduction to Linear Algebra.

 

Assistant Professor at Florida International University, 2004-2007

 

Graduate Courses taught:

  MAS 5145 Applied Linear Algebra,

  MAS 5311 Graduate Algebra,

  MAS 5312 Galois Theory,

  MAT 5907 Independent Study (on selected topics in Algebra).

 

Undergraduate Courses taught:

  MAP 2312 Differential Equations,

  MAS 3105 Linear Algebra,

  MAS 4301 Algebraic Structures,

  MAS 4302 Topics in Algebraic Structures,

  MAT 4905 Independent Study (on selected topics in Algebra).

 

Post Doctoral Fellow at the University of Missouri-Columbia, 2001-2004.

 

  MTH 60 Finite Mathematics,

  MTH 201 Calculus III,

  MTH 226 Discrete Mathematics.

 

Graduate Teaching Assistant at Michigan State University, 1995-2001.

 

             Courses taught (as primary instructor):

               MTH 103 College Algebra,

               MTH 124 Survey of Calculus with Applications I,

               MTH 126 Survey of Calculus with Applications II,

               MTH 201 Mathematical Investigations I,

               MTH 235 Differential Equations.

 

Led recitations for MTH 116 College Algebra and Trigonometry, Fall 1995.

 

Lead Teaching Assistant for MTH 124 during Fall 1999, Spring and Fall 2000 (responsible for writing exams and the uniform final for approximately 1500 students, and for visiting other TA’s classes and giving them feedback on their lectures).

 

 

last updated January 2014

Department of Mathematics                                                                    

New York City College of Technology

The City University of New York

300 Jay Street, N711

Brooklyn, NY 11201

Tel:  (718) 260-4965

Fax: (718)  254-8537

E-mail: lghezzi@citytech.cuny.edu

http://websupport1.citytech.cuny.edu/faculty/lghezzi/