Stefano Silvestri Ph.D.

I first thought of becoming a mathematician during my last year of highschool, thanks to a couple of special programs with Rome’s Third University. The thought then became a goal while an undergraduate at Boston University once Professor R.L. Devaney agreed to supervise me on a research project.

• Pérez, R. A. and Silvestri, S. "A Catalog of Geometric Progression References in the Historical Record."
  ---in preparation---
• Pérez, R. A. and Silvestri, S. "Accessibility of the Boundary of the Thurston Set." Experimental Mathematics 32 (2), pp.405--422 (2023).
  Journal DOI:10.1080/10586458.2021.1974984 Preprint (arXiv)

  abstract

  Consider two objects associated to the Iterated Function System (IFS) $\{1+\lambda z,-1+\lambda z\}$: the locus $\mathcal{M}$ of parameters $\lambda \in \mathbb{D}\setminus \{0\}$ for which the corresponding attractor is connected; and the locus ${\mathcal{M}}_0$ of parameters for which the related attractor contains $0$. The set $\mathcal{M}$ can also be characterized as the locus of parameters for which the attractor of the IFS $\{1+\lambda z,\lambda z,-1+\lambda z\}$ contains ${\lambda }^{-1}$. Exploiting the asymptotic similarity of $\mathcal{M}$ and ${\mathcal{M}}_0$ with the respective associated attractors, we give sufficient conditions on $\lambda \in \partial \mathcal{M}$ or $\partial {\mathcal{M}}_0$ to guarantee it is path accessible from the complement $\mathbb{D}\setminus \mathcal{M}$.
• Alibeik, M., Nezamuddin, O., Rubin, M., Wheeler, N., Silvestri, S., dos Santos, E. "Airgap-less electric motor: A solution for high-torque low-speed applications." IEEE International Electric Machines and Drives Conference (IEMDC) pp.1--8 (2017).
  Journal DOI:10.1109/IEMDC.2017.8002357 Preprint (PDF )

  abstract

  This paper proposes a new category of electric motors able to generate high torque with reduced volume, i.e., high torque density. Such a new design is denominated as an airgapless electrical motor since the rotor touches the stator as it spins. Due to its zero airgap, the proposed motor will maximize the generated torque, allowing such type of motors to be competitive in applications where hydraulic motors are prevalent, i.e., low-speed and high-torque requirements. Unlike hydraulic motor systems that face two major problems with their braking system and also with low efficiency due to a large number of energy conversion stages (i.e., motor-pump, hydraulic connections and the hydraulic motor itself), the proposed electric motor converts electrical energy directly to mechanical energy with no extra braking system necessary and with higher efficiency. A proof-of-concept electric motor prototype along with its drive system is built to validate the theoretical assumptions proposed in this paper.
• Blanchard, P., Cuzzocreo, D., Devaney, R. L., Fitzgibbon, E., and Silvestri, S. "A Dynamical Invariant for Sierpiński Cardioid Julia Sets." Fundamenta Mathematicae 226, pp.253--277 (2014).
  Journal DOI:10.4064/fm226-3-5 Preprint (PDF )

  abstract

  For the family of rational maps $z^n+\lambda /z^n$ where $n\ge 3$, it is known that there are infinitely many copies of the Mandelbrot set that are buried in the paramenter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located in the parameter plane have conjugate dynamics. We produce a dynamical invariant that explains why these maps have different dynamics.
• Silvestri, S. "Non Homeomorphic Julia Sets of Singularly Perturbed Rational Maps." Pi Mu Epsilon Journal 13:10, (2014).
  Journal Preprint (PDF )

  abstract

  In this paper we investigate the Julia sets of singularly perturbed complex rational maps of the form $f(z)=z^2+\lambda /z^2$. We will show that two maps drawn from different main cardioids of accessible baby Mandelbrot sets containing a cycle of period $4$ are not homeomorphic on their Julia sets, unless these cardioids are complex conjugates of one another.
• Fitzgibbon, E. and Silvestri, S. "Rational Maps: Julia Sets of Accessible Mandelbrot Sets are not Homeomorphic." Topology Proceedings (2013).
  Preprint (PDF )

  abstract

  In this paper we investigate the Julia sets of singularly perturbed complex rational maps of the form $f(z)=z^n+\lambda /z^d$. We will show that, for the case $n=d=2$, two maps drawn from main cardioids of distinct accessible Mandelbrot sets containing a cycle of period $m$ do not have homeomorphic Julia sets, unless these cardioids are complex conjugates of one another.
• Bose, K., Cox, T., Silvestri, S., and Varin, P. "Invasion Front and Pattern Formation in a Model of Chemotaxis in One and Two Dimensions." SIAM Undergraduate Research Online 6, (2013).
  Journal DOI:10.1137/12S012008 (PDF )

  abstract

  The purpose of this paper is to explore spatio-temporal pattern formation via invasion fronts in the one and two dimensional Keller-Segel chemotaxis model. In the one-dimensional case, simulations show that solutions that begin near an unstable equilibrium evolve into periodic patterns. These in turn evolve into new patterns through a process known as coarsening. In the two-dimensional case, we encounter only periodic patterns in the wake of the initial front. Transverse patterning only arises as a result of a transverse instability of these periodic patterns from the leading invasion front.

The talks with an indicate that I have been invited to it.

• "Rational Maps: Julia Sets of Accessible M-Sets Are Not Homeomorphic." Fitzgibbon, E. and Silvestri S. Midwest Dynamical System (MWDS) 11-2013. (PDF )

• HAC Travel-To-Present Grant from Holcomb Awards Committee and College of Liberal Arts & Science at Butler University 2019.
• Best Student Presentation from Postgraduate Conference in Complex Dynamics 03-2019.
• Outstanding Graduate Student Teaching Award from IUPUI School of Science 2018.
• Certificate in College Teaching from Center for Teaching and Learning: Emerging Scholars of College Instruction Program 2017.

My Erdös number is 4 (check yours using the AMS MathSciNet’s free Collaboration Distance tool):
following either Erdös, P. > Dixmier, J. > Duoady, A. > Devaney, R.L. > Silvestri, S. or Erdös, P. > Alladi, K. > Andrews, G.E. > Pérez, R.A. > Silvestri, S.

Check out my mathematical family tree at Mathematics Genealogy Project. Here are some mathematician in my tree: Friedrich Leibniz, Karl Theodor Wilhelm Weierstraß, Carl Gustav Jacob Jacobi, Carl Gottfried Neumann, Solomon Lefschetz, John Willard Milnor, and Mikhail Yu Lyubich.