# Maksym Fedorchuk

Assistant Professor

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

Department of Mathematics
Boston College
Carney Hall 324
140 Commonwealth Avenue
Chestnut Hill, MA 02467

 Curriculum Vitae Research Teaching Meetings Travel

Announcement: Spring 2015 AGNES conference will take place at Boston College from Friday, March 20 to Sunday, March 22.
The conference will be preceded by a mini-school for graduate students (10am-3pm on Friday, March 20).

### 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. 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), preprint, 49pp.

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

3. 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), preprint, 30pp.

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

5. A semiampleness criterion for divisors on $\overline{M}_{0,n}$. Submitted, a slightly different version on arXiv:1407.7839.
An accompanying SAGE worksheet

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

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

8. New nef divisors on $\overline{M}_{0,n}$ on arXiv:1308.5993 (a revision with more general results, based on the item (16) above, is forthcoming).
This proves Conjecture 1.7 from the earlier
Type A level one conformal blocks divisors revisited, 2011.

9. 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)

10. 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.

11. 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

12. Moduli spaces of hyperelliptic curves with A and D singularities
Mathematische Zeitschrift, doi:10.1007/s00209-013-1201-6, 2013 (journal version)

13. Stability of 2nd Hilbert points of canonical curves (joint with David Jensen)
Int. Math. Res. Notices, 2013 (2013) no. 22: 5270-5287. doi: 10.1093/imrn/rns204 (journal version)

14. The final log canonical model of the moduli space of stable curves of genus four
International Mathematics Research Notices (2012) DOI:10.1093/imrn/rnr242, 23pp (journal version)

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

16. 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

17. 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)

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

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

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

### Conferences and seminars

I co-organize the following Algebraic Geometry seminars:

Keep track of Algebraic Geometry in Boston and subscribe to the calendar of events using the following links HTML, ICAL, XML

#### Meetings organized

• BC-Northeastern Algebraic Geometry Mini-Conference (with Ana-Maria Castravet, Dawei Chen, Brian Lehmann, Emanuele Macri, Alina Marian), April 25, 2015
• Graduate mini-school leading to AGNES Spring 2015 (with Dawei Chen, Brian Lehmann, Jason Starr), March 20, 2015
• AGNES Spring 2015 at Boston College (with Dawei Chen and Brian Lehmann), March 20--22, 2015
• AGNES Fall 2013 at Boston College (with Dawei Chen and Alina Marian), October 25--27, 2013
• Special Session on Moduli Spaces in Algebraic Geometry at Boston College (with Dawei Chen, Joe Harris, Yu-Jong Tzeng), April 6--7, 2013
• Workshop on Log minimal model program for moduli spaces at the American Institute of Mathematics (AIM) (with Jarod Alper, Brendan Hassett, and David Smyth),
December 10--14, 2012

### Teaching

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

#### Current teaching and undergraduate research supervision (Spring 2015)

• MATH 312 Algebra II (undergraduate)
• MATH 496 Honors Thesis

#### Past teaching at Boston College

• 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