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Nicolas Robles

J L Doob Research Assistant Professor

Contact Information

Office Address:
241, Illini Hall
Telephone: 217-265-5225
E-mail: nirobles ... this school

Mailing Address:
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, IL 61801

About me

Since July 2018, I have been a quant analyst at BofA in Chicago.

From August 2015 to August 2018, I was a Doob postdoc in the Mathematics Department of the University of Illinois at Urbana-Champaign. I also worked for Wolfram and for the CQF program.

In May 2015, I finished my doctoral thesis at the I-Math of UZH in Zurich, Switzerland. My supervisors were Alberto Cattaneo and Ashkan Nikeghbali and I was partially supported by the Forschungskredit grant K-71104-04-0.

Before joining the I-Math I took Part III of the Mathematical Tripos at the University of Cambridge (my thesis was on quantum rate-distortion theory).

Prior to that, I also completed the highly, highly recommended M.Sc. in Quantum Fields and Fundamental Forces at Imperial College London (this time my thesis was on zeta function regularization).

Previously, I worked in investment banking in London and Zurich (JPMorgan, Nomura and UBS).

Research

My interests are primarily in number theory, theoretical physics and quantitative finance. I like to keep it as orthogonal as possible.

Publications

POST-DOCTORAL PAPERS (2015 - 2018)

(17) Breaking the 1/2 barrier for the twisted second moment of Dirichlet L-functions
joint work H. M. Bui, K. Pratt and A. Zaharescu
Advances in Mathematics (doi.org/10.1016/j.aim.2020.107175)

(16) Unexpected average values of generalized von Mangoldt functions in residue classes
joint work with A. Roy
Journal of the Australian Mathematical Society (10.1017/S1446788719000715)

(15) Random permutations with logarithmic cycle weights
joint work D. Zeindler
Ann. Inst. Henri Poincaré Probab. Stat. (1593137316)

(14) More than five-twelfths of the zeros of ζ are on the critical line
joint work with K. Pratt, A. Zaharescu and D. Zeindler
Research in the Mathematical Sciences (10.1007/s40687-019-0199-8)

(13) On mean values of mollifiers and L-functions associated to primitive cusp forms
joint work with P. Kühn and D. Zeindler
Mathematische Zeitschrift (10.1007/s00209-018-2099-9)

(12) Perturbed moments and a longer mollifier for critical zeros of ζ
joint work with K. Pratt
Research in Number Theory (10.1007/s40993-018-0103-4)

(11) Zeros of normalized combinations of ξ(k)(s) on Re(s)=1/2
joint work with S. Chaubey, A. Malik and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2017.12.045)

(10) Polynomial partition asymptotics
joint work with A. Dunn
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2017.10.051)

(9) The largest gap between zeros of entire L-functions is less than 41.54
joint work with P. Kühn and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2016.12.007)

(8) On a mollifier of the perturbed Riemann zeta-function
joint work with P. Kühn and D. Zeindler
Journal of Number Theory (10.1016/j.jnt.2016.09.022)

(7) Moments of averages of generalized Ramanujan sums
joint work with A. Roy
Monatshefte für Mathematik (10.1007/s00605-016-0907-z)

DOCTORAL PAPERS (2011 - 2015)

(6) Koshliakov kernel and identities involving the Riemann zeta function
joint work with A. Dixit, A. Roy and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2015.11.007)

(5) Twisted second moments of the Riemann zeta-function and applications
joint work with A. Roy and A. Zaharescu
Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2015.08.064)

(4) Explicit formulas of a generalized Ramanujan sum
joint work with P. Kühn
International Journal of Number Theory (10.1142/S1793042116500238)

(3) Zeros of combinations of the Riemann ξ-function on bounded vertical shifts
joint work with A. Dixit, A. Roy and A. Zaharescu
Journal of Number Theory (10.1016/j.jnt.2014.10.004)

(2) Zeta functions on tori using contour integration
joint work with E. Elizalde, K. Kirsten and F. L. Williams
Int. J. Geom. Methods Mod. Phys. (10.1142/S021988781550019X)

(1) On a class of functions that satisfies explicit formulae involving the μ function
joint work with P. Kühn and A. Roy
The Ramanujan Journal (10.1007/s11139-014-9608-1)

Teaching

(8) Differential Equations
Summer 2018, MATH441 website link

(7) Calculus II
Spring 2018, MATH231 website link

(6) Calculus III
Fall 2017, MATH241 website link

(5) Multivariable Calculus (Harvard University)
Summer 2017, MATH21a (Oliver Knill) website link

(4) Analytic Theory of Numbers II
Spring 2017, MATH532 website link

(3) Probability Theory
Fall 2016, MATH461 website link

(2) Introduction to Matrix Theory
Spring 2016, MATH225 website link

(1) Elementary Theory of Numbers
Fall 2015, MATH453 website link