PURE Math Interns

2012

 
2012_Intern_Photo.html

Intern Advisors: Dr. Brian Loft - Sam Houston State University

                            Dr. Efren Ruiz - University of Hawai`i at Hilo

Graduate Assistant: Mauricio Rivas - University of Houston


Interns

Joyce Auau - University of Hawai`i at Hilo

Tony Coie - Cal Poly Pomona

Briana Flores - Pacific Univeristy

Julio Hernandez - California State University, Chico

Lindsay Hill - Baker University

Sam Jean-Batiste - Emory University

Alyssa Loving - University of Hawai`i at Hilo

Erik Maki - Florida Institute of Technology

Connie Maluwelmeng - University of Guam

Kennesha Saito - University of Oregon

Octavious Talbot - More House

Mitchell Walker -University of Hawai`i at Manoa

Projects


Combinatorial Laplacian and Discrete Morse Theory            

Erik Maki and Kennesha Saito, directed by Dr. Brian Loft


Abstract               Presentation


A Medical Application of Discrete Morse Theory            

Briana Flores, Julio Hernandez, and Lindsay Hill, directed by Dr. Brian Loft


Abstract               Presentation


Discrete Morse Theory and Spaces of Trees            

Connie Maluwelmeng, Octavious Talbot, and Mitchell Walker, directed by Dr. Brian Loft


Abstract               Presentation


Leavitt path algebras associated with acyclic graphs

Joyce Auau and Antonio Coie, directed by Dr. Efren Ruiz


Abstract               Presentation


The characterization of properly purely infinite algebras

Alyssa Loving and Sam Jean-Baptiste, directed by Dr. Efren Ruiz


Abstract               Presentation

    The Interns topics introduced twelve undergraduates to the theory of algebras (leavitt-path algebras) and discrete morse theory. The Interns Program was directed by Dr. Brian Loft and Dr. Efren Ruiz, with assistance from Mauricio Rivas.

Course Descriptions

Discrete Morse Theory - This course will relate the topology of a space to the properties of real valued functions defined on that space.  We will examine the fundamentals of two versions of Morse theory: the smooth and discrete versions.  After a brief introduction to the principles of topology, the theory will be used in several applications from biology to computer science. 


Theory of Algebras - In this course, we will study algebraic structures in which addition, multiplication, and scalar multiplication are defined.  An example of an algebra is the set of all complex numbers.  One can add and multiple two complex numbers and a get back a complex number.  One can multiple a complex number with a real number and get a complex number.  We will study general properties of these algebra structures.  We will also study special algebras called Leavitt path algebras.  Leavitt path algebras are algebras associated to directed graphs.  These algebras are particular nice because many of the properties can be described using the directed graphs.