I am an Associate Professor in the Department of Mathematics at the University of Mississippi.

In May 2008, I completed a Ph.D. under the supervision of Professor Steven M. Gonek at the University of Rochester.

Here is my CV (last updated April 2015).

- Email: mbmilino "at" olemiss "dot" edu
- Phone: 662.915.7071
- Office: Hume 304

- Office Hours: Tues. 1:30-2:30pm, Thurs. 1:30-2:30pm, or by appointment.

Course | Time | Room |
---|---|---|

Math 263 -- Calculus III |
TTh 9:30am -- 10:45am |
Hume 113 |

Math 513 -- Theory of Numbers I |
TTh 11:00am -- 12:15pm |
Hume 321 |

- Course information is posted on Blackboard.

Previous teaching at the University of Mississippi:

Math 261 - Calculus I (F'08, F'09, F'10, F'13),

Math 261 - Calculus I, Honors College (F'15x2, F'16),

Math 263 - Calculus III (S'09, S'10, S'11, S'14, F'14),

Math 263 - Calculus III, Honors College (F'10),

Math 459 - Introduction to Complex Analysis (F'11, F'12, F'16)

Math 513 - Theory of Numbers, I (S'09, S'10, S'11, S'12, S'13, S'15),

Math 514 - Theory of Numbers, II (F'09),

Math 625 - Abstract Algebra, I (F'14),

Math 626 - Abstract Algebra, II (S'15),

Math 655 - Theory of Functions of a Complex Variable, I (F'11, F'12, F'13),

Math 656 - Theory of Functions of a Complex Variable, II (S'12, S'13, S'14),

Math 597/697/797 - Reading courses in Number Theory (Continuously since S'09)

- Previous
teaching at the University of Rochester:

Math 142 - Calculus II (F'05),

Math 161 - Calculus IA (F'04)

Research:

My Google Scholar profile.

Papers:

- Gaps between zeros of the Riemann zeta-function,
*(with Hung M. Bui)*

submitted for publication. - Bandlimited approximations and estimates for the
Riemann zeta-function,
*(with E. Carneiro and A. Chirre)*

submitted for publication. - Linear
relations of zeros of the zeta function,

Oberwolfach Reports, no. 53, to appear. - Hilbert
spaces and the pair
correlation of
zeros
of the Riemann zeta-function,
*(with E. Carneiro, V. Chandee and F. Littmann)*

Journal für die reine und angewandte Mathematik (Crelle's Journal), 725 (2017), 143--182. - A note on
the zeros of zeta and L-functions
*, (with Emanuel Carneiro and Vorrapan Chandee)*

Mathematische Zeitschrift, 281 (2015), no. 1-2, 315--332. - A
hybrid Euler-Hadamard product
and moments
of ζ'(ρ),
*(with Hung M. Bui and Steven M. Gonek)*

Forum Mathematicum, 27 (2015), no. 3, 1799--1828. - Simple
zeros of
modular L-functions,
*(with Nathan Ng)*

Proceedings of the London Mathematical Society, 109 (2014), no. 6, 1465--1506. - Lower
bounds for
moments
of ζ'(ρ),
*(with Nathan Ng)*

International Mathematics Research Notices (IMRN), (2014), no. 12, 3190--3216. - Moments of products of
automorphic L-functions,
*(with Caroline Turnage-Butterbaugh)*

Journal of Number Theory, 139 (2014), 175--204. - On
Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis,
*(with Hung M. Bui and Stephen J. Lester)*

Journal of Mathematical Analysis and Applications, 409 (2014), no. 1, 244--253. - Bounding S(t)
and S
_{1}(t) on the Riemann Hypothesis,*(with Emanuel Carneiro and Vorrapan Chandee)*

Mathematische Annalen, 356 (2013), no. 3, 939--968. - A note on simple a-points
of L-functions,
*(with Steven M. Gonek and Stephen J. Lester)*

Proceedings of the American Mathematical Society, 140 (2012), no. 12, 4097--4103. - A note on
a conjecture of
Gonek,
*(with Nathan Ng)*

*Functiones et Approximatio, Commentarii Mathematici*, 46 (2012), no. 2, 177--187. - Moments
of the Riemann
zeta-function at its relative extrema on the critical line,

Bulletin of the London Mathematical Society, 43 (2011), no. 6, pp. 1119--1129. - Central values of
derivatives of Dirichlet L-functions,
*(with Hung M. Bui)*

*International Journal of Number Theory***7**(2011), no. 2, pp. 371--388. - A note on the gaps between
consecutive zeros of the Riemann zeta-function,
*(with Hung M. Bui and Nathan Ng)*

**138**(2010), no. 12, pp. 4167--4175. - Upper bounds for
moments of ζ'(ρ),

**42**(2010), no. 1, pp. 28--44. - Mean-Value Estimates
for the Derivative of the Riemann Zeta-Function,

- Extreme values of S(t) in the
theory of the Riemann zeta-function,
*(with Hung M. Bui and Maksym Radziwill)*

In preparation. - Moments of the Riemann
zeta-function and its derivatives,
preprint available upon request.

(This manuscript computes the lower order terms in the second moment of ζ'(ρ) as announced

in section 7.1 of Conrey & Snaith's "Applications of the L-functions ratios conjectures," link.)

Some of my preprints are available on the arXiv. The versions that appear there may not be up to date.

- NSA Young Investigator Grant H98230-16-1-0311 (2017-2019)
- US Junior Oberwolfach Fellow, sponsored by NSF (Sept. 2017)
- SEC Faculty Travel Grant (2016-2017)
- US Junior Oberwolfach Fellow, sponsored by NSF (Nov. 2016)

- NSA Young Investigator Grant H98230-15-1-0231 (2015-2017)
- NSA Young Investigator Grant H98230-13-1-0217 (2013-2015)
- SEC Faculty Travel Grant (2013-2014)

- AMS-Simons Travel Grant (2011-2013)
- MRC Collaboration Grant (with Maksym Radziwill), sponsored by AMS / NSF (2012-2013)
- University of Mississippi College of Liberal Arts Summer
Research Grant:

Every summer eligible -- Summer 2009, Summer 2010, Summer 2012

- Michael Azlin, M.S., May 2011
(co-supervised with Nathan Jones).

Current position: Instructor, University of Mississippi, Fall 2011 - present. - Caroline
Turnage-Butterbaugh,
Ph.D. May 2014.

GAANN fellow, Class Marshal, and a recipient of a Graduate Student Achievement Award.

Currently: Elliott Research Assistant Professor, Duke University, Fall 2015 - present. - Zhenchao Ge, M.S. Dec. 2015.

Current position: Ph.D. student, University of Mississippi.

- Automorphic Froms and Arithmetic Workshop, Oberwolfach, Sept. 2017 (tentative).
- Number Theory and Representation Theory Seminar, University of Missouri, Jan. 19, 2017.
- Joint
Mathematics Meetings, (invited talk) Atlanta, GA, Jan. 2017.

- Algebraic
Geometry & Number Theory Seminar, Rice University, Dec. 6, 2016.

- Analytic Number Theory Workshop, (invited talk) Oberwolfach, Nov. 2016.
- AIM Workshop, "Moments of zeta and correlations of divisor sums," Sept. 2016.
- Visiting Researcher, Stanford University, April 2016.
- Number Theory Seminar, University of Manchester, March 10, 2016.
- Analysis Seminar, Cardiff University, March 4, 2016.

- Heilbronn
Seminar, University of Bristol, March 2, 2016.

- Number
Theory and Combinatorics Seminar, University of Lethbridge, Feb. 1,
2016.

- ICERM Workshop, "Computational Aspects of L-functions," Nov. 2015, Brown University.
- UNC-Duke
Number Theory Seminar, Duke University, September 30, 2015.

- UIUC
Number Theory Seminar, University of Illinois, September 10, 2015.

- International Conference in Number Theory and Physics, (invited talk) June 2015. IMPA, Rio de Janeiro, Brazil.
- Research
in Teams at BIRS, May 24-31, 2015 (with Andrew Booker and Nathan Ng).

- Number
Theory and Representation Theory Seminar, University of Missouri,
March 10, 2015.

- AIM Workshop, "Bounded gaps
between primes," November 2014, Palo Alto, CA.

- Bateman/Halberstam
conference, University of Illinois, June 5-7, 2014.

- Heilbronn
Seminar, May 21st, 2014. Bristol, UK.

- University of Georgia Number Theory Seminar, April 16th, 2014. Athens, GA.
- Ohio State Number Theory Seminar, February 17th, 2014. Columbus, OH.
- AMS/MAA Joint Math Meetings, Jan. 14th-18th, Baltimore, MD.

- Analysis Seminar, IMPA, August 29th, 2013. Rio de Janeiro, Brazil.
- Visiting Researcher, CRM, July 18th-23rd, 2013. Montreal, Quebec.
- Quebec-Vermont Number Theory Seminar, November 8th, 2012. Montreal, Quebec.
- Ohio State Number Theory Seminar, October 22nd, 2012. Columbus, OH.

In January 2012, I co-organized a special session on multiplicative number theory with Leo Goldmakher, Jonathan Kish, and Paul Pollack at the AMS-MAA joint math meetings in Boston. The details can be found here.