Maksym Fedorchuk

Assistant Professor

Email: fedorchm[at]bc.edu
Tel: 617-552-3757

Department of Mathematics
Boston College
Maloney Hall 570
140 Commonwealth Avenue
Chestnut Hill, MA 02467

 Curriculum Vitae Research Teaching Meetings Outreach Travel

Research

I am an algebraic geometer. My research is partially supported by the NSF grant DMS-1259226 and Alfred P. Sloan Research Fellowship.

Publications and preprints

1. GIT semistability of Hilbert points of Milnor algebras.
The old title and version is GIT semistability of the gradient of a homogeneous form, on arXiv:1508.06991, submitted, August 2015.

2. Semiampleness criteria for divisors on $\overline{M}_{0,n}$. Submitted.
A major revision (June 2015) of an earlier arXiv:1407.7839 now incorporates new results and Item (13) below.
An accompanying SAGE worksheet

3. Log minimal model program for the moduli space of stable curves: The second flip (joint with Jarod Alper, David Smyth, and Fred van der Wyck), submitted, 49pp.

4. Existence of good moduli spaces with applications to the log minimal program for $\overline{M}_{g,n}$ (joint with Jarod Alper and David Smyth), submitted, 28pp.

5. Projectivity of the moduli space of $\alpha$-stable curves and the log minimal program for $\overline{M}_{g,n}$ (joint with Jarod Alper and David Smyth), submitted, 30pp.

6. Integrated version of the above three papers on arXiv:1308.1148

7. Toward GIT stability of syzygies of canonical curves (joint with Anand Deopurkar and David Swinarski), version as of February 2015.
Algebraic Geometry, to appear, 2015. An earlier version on arXiv:1401.6101

8. Groebner techniques and ribbons (joint with Anand Deopurkar and David Swinarski),
Albanian J. Math. 8 (2014), no. 2, 55-70 (journal version)

9. New nef divisors on $\overline{M}_{0,n}$ on arXiv:1308.5993.
This proves Conjecture 1.7 from the earlier
Type A level one conformal blocks divisors revisited, 2011.

10. Singularities with G_m-action and the log minimal model program for $\overline{M}_g$ (joint with Jarod Alper and David Smyth),
Journal für die reine und angewandte Mathematik, DOI: 10.1515/crelle-2014-0063, August 2014 (ahead of print at Crelle's Journal)

11. GIT of genus five canonical curves (joint with David Smyth) on arXiv:1302.4804
A Celebration of Algebraic Geometry, 281-310, Clay Mathematics Proceedings, vol. 18, CMI/AMS, 2013.

12. Moduli spaces of hyperelliptic curves with A and D singularities
Mathematische Zeitschrift 276 (2013) no. 1--2, 299-328. (journal version)

13. Finite Hilbert stability of (bi)canonical curves (joint with Jarod Alper and David Smyth)
Inventiones mathematicae 191 (2013) no. 3, 671-718 (journal version)
*The final publication is available at www.springerlink.com

14. Stability of 2nd Hilbert points of canonical curves (joint with David Jensen)
Int. Math. Res. Notices, 2013 (2013) no. 22: 5270-5287 (journal version)

15. The final log canonical model of the moduli space of stable curves of genus four
Int. Math. Res. Notices, 2012 (2012) no. 24: 5650-5672 (journal version)

16. Cyclic covering morphisms on $\overline{M}_{0,n}$ (with an appendix by Anand Deopurkar, 2013); an older version on arXiv:1105.0655

17. Alternate compactifications of moduli spaces of curves (joint with David Smyth) on arXiv:1012.0329
in Handbook of Moduli: Volume I, 331-414, editors Gavril Farkas and Ian Morrison, Adv. Lect. Math. (ALM), 24, Int. Press, Somerville, MA, 2013

18. Moduli spaces of weighted stable curves and log canonical models of M_{g,n}
Math. Res. Lett., 18 (2011) no. 4, 663-675 (journal version)

19. Ample divisors on moduli spaces of pointed rational curves (joint with David Smyth)
J. Algebraic Geom., 20 (2011) no. 4, 599-629 (journal version)

20. Severi varieties and the moduli space of curves (Harvard dissertation) on arXiv:0710.1623

21. Rigidity and polynomial invariants of convex polytopes (joint with Igor Pak)
Duke Math. J., 129 (2005), no. 2, 371-404 (journal version)

Meetings

Seminars

I co-organize the following Algebraic Geometry seminars:

Meetings organized

I have taught a variety of undergraduate and graduate courses at Boston College (2012-present) and Columbia University (2008-2012).

Fall 2015

I am on leave supported by Boston College Faculty Fellowship

Summer 2015

• Undergraduate research project for three students (supported by the Boston College Undergraduate Research Fellowship program)

Past teaching at Boston College

• MATH 312 Algebra II (undergraduate), Spring 2015
• MATH 496 Honors Thesis, Spring 2015
• MATH 490 Readings and Research (undergraduate reading course on plane algebraic curves and curve singularities), Spring 2015
• MATH 311 Algebra I (undergraduate), Fall 2014
• MATH 845 Topics in Algebra and Number Theory (graduate course on complex algebraic surfaces), Fall 2014
• MATH 496 Undergraduate Honors Thesis, Fall 2014
• MT 430 Intro to Number Theory, Spring 2014
• MT 807 Algebra II (graduate), Spring 2014
• MT 105 Calculus II-AP, Fall 2013
• MT 430 Intro to Number Theory, Spring 2013
• MT 202 Multivariable Calculus, Fall 2012
• MT 806 Algebra I (graduate), Fall 2012

Outreach

I am organizing a Math Teachers' Circle at Boston College (for high-school and pre-service teachers) that is a part of the AIM's MTC Network.
Details coming soon. Contact me in the meantime if you are interested.

Travel

• Yale BATMOBYLE, December 10
• BC Faculty Fellowship leave in Fall 2015: Max Planck Institute in Bonn (September 29 -- November 3, 2015),
Roma Tre (November 3 -- November 15), ANU (November 24-December 8)
• Humboldt University AG seminar (October 28), University of Bonn AG seminar (October 29),
Università di Firenze AG seminar (November 9), Roma Tre AG seminar (November 12)
• Stony Brook AG seminar (September 9) and Northeastern GASC seminar (September 14)
• SIAM Algebraic Geometry Mini Symposium: Computational Approaches to GIT and Moduli Theory, Daejeon, Korea, August 3--6, 2015