241, Illini Hall

niroblesillinois.edu

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

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

From August 2015 to August 2018, I was a Doob postdoc. I was also a contractor for Wolfram and for the CQF program.

In May 2015, I defended my doctoral thesis at UZH in Switzerland. My supervisors were Alberto Cattaneo and Ashkan Nikeghbali.

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) as well as the highly recommended M.Sc. in Quantum Fields and Fundamental Forces at Imperial College London (this time my thesis was on zeta function regularization). Simultaneously, I worked in investment banking at JPMorgan, Nomura and UBS.

*Differential Equations*

Summer 2018, MATH441 departmental website link*Calculus*II

Spring 2018, MATH231 website link*Calculus*III

Fall 2017, MATH241 website link*Multivariable Calculus*(Harvard)

Summer 2017, MATH21a website link*Analytic Theory of Numbers*II

Spring 2017, MATH532 website link*Probability Theory*

Fall 2016, MATH461 website link*Introduction to Matrix Theory*

Spring 2016, MATH225 website link*Elementary Theory of Numbers*

Fall 2015, MATH453 website link

*Breaking the*1/2*barrier for the twisted second moment of Dirichlet L-functions*

joint work H. M. Bui, K. Pratt and A. Zaharescu, submitted, (arXiv: 1808.10803)*Unexpected average values of generalized von Mangoldt functions in residue classes*

joint work with A. Roy, to appear in Journal of the Australian Mathematical Society*Random permutations with logarithmic cyclic weights*

joint work with D. Zeindler, to appear in Annales de l'Institut Henri PoincarÃ©, ProbabilitÃ©s et Statistiques, (arXiv: 1806.04700)*More than five-twelfths of the zeros of*ζ*are on the critical line*

joint work with K. Pratt, D. Zeindler and A. Zaharescu, to appear in Research in the Mathematical Sciences, (arXiv: 1802.10521)*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)*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)*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)*Polynomial partition asymptotics*

joint work with A. Dunn, Journal of Mathematical Analysis and Applications (10.1016/j.jmaa.2017.10.051)*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)*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)*Moments of averages of generalized Ramanujan sums*

joint work with A. Roy, Monatshefte für Mathematik (10.1007/s00605-016-0907-z)

*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)*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)*Explicit formulas of a generalized Ramanujan sum*

joint work P. Kühn, International Journal of Number Theory (10.1142/S1793042116500238)*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)*Zeta functions on tori using contour integration*

joint work with E. Elizalde, K. Kirsten and F. L. Williams, International Journal of Geometric Methods in Modern Physics (10.1142/S021988781550019X)*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)

UIUC Number Theory seminar

UIUC Graduate Student Number Theory Seminar

AMS

PhD comics