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Academic Research

As a Loyola student, you have the opportunity to work alongside our talented professors to partner in collaborative research. Learn more about some recent research and projects currently underway.

A Within Host Model of Dengue Virus Infection

Dr. Jeremy Thibodeaux and senior mathematics student Michael Hennessey have derived a system of differential equations that model certain blood cell and particle populations in the body when it is infected with Dengue virus. The model aims to capture the relevant physiological processes to provide researchers a tool to develop more effective antiviral drugs and treatments in the fight against Dengue Fever.

Zero Divisor Graphs

My research involves using graph theory to study rings.  A ring is a set within which we can add, subtract, and multiply. Strangely enough, sometimes in a ring the product of two non-zero elements is zero! For example, this can happen when we multiply matrices.

Faculty research to be published in Mexican Math. Society journal

Dr. Michael Kelly is currently working on research in the area of topology known as Fixed Point Theory.  A collaboration with Professor D. Goncalves of the University of Sao Paulo, Brasil has lead to a research article which will appear in the journal Bulletin of the Mexican Math. Society.   This collaboration is ongoing and also involves a research project which is related to the graphic on the left. 

 

Student research project exploring idempotents

Second year mathematics major Linda Hexter is currently working under the supervision of Dr. Kelly.  She is working on a project exploring idempotent matrices and implications to a problem in fixed point theory regarding homotopy idempotents.

Professor and Student Collaborate on Mathematics Investigation

Professor Thibodeaux and senior student Savannah Logan '14, worked on a project to investigate relationships between derivatives and algebraic structures called zero divisors. They first derived a formula for the number of zero divisors in the set of upper triangular matrices whose entries are from some subset of the whole numbers. They then determined the rate at which this number grows as a function of the size of the matrices and the size of the subset of whole numbers.

Zero Divisor Graphs for Commutative and Noncommutative Rings

Zero divisors are objects that arise in one of the most abstract areas of mathematics. Surprisingly, investigators are able to study zero divisors using computational and geometric techniques. One of the geometric techniques involves diagrams called zero divisor graphs. Since 1988 there has been a plethora of articles on this topic. Dr. Thibodeaux and Dr.

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