*Spring 2017 Lectures and Events*

Date |
Room |
Speaker |
Title |

Jan 12 4:30pm |
LC 412 | (Department Colloquium) | |

Jan 19 4:30pm |
LC 412 | Sameed Ahmed |
Mathematical Modeling of HER2 Signaling Pathway: Implications for Breast Cancer TherapySIAM Student Chapter: Why You Should Participate! |

Feb 16 4:30pm |
LC 412 | (Combinatorics Superseminar) | |

Feb 21 4:30pm |
LC 412 | Candace Bethea |
The Grothendieck Group: What is it and Where to Find it |

Mar 2 4:30pm |
LC 412 | Joe Foster |
An Introduction to Minimal Surfaces |

Spring Break | |||

Mar 16 4:30pm |
LC 412 | (Combinatorics Superseminar) | |

Mar 21 4:30pm |
LC 412 | Julie Lang |
The Spring Number of a Graph |

Mar 23 4:30pm |
LC 412 | (Special Event) | |

Mar 30 4:30pm |
LC 412 | Various Speakers |
Invitations to Upcoming Graduate Courses |

Apr 6 4:30pm |
LC 412 | Jeremiah Southwick |
Residue Completeness of Generalized Fibonacci Sequences mod m |

Apr 20 4:30pm |
LC 412 | Various Speakers |
Qualification and Comprehensive Exam Panel |

**More events to come!**

The graduate colloquium will usually run Tuesdays or Thursdays at 4:30pm.

If you would like to speak in the seminar, please email Alex Duncan.

** Sameed Ahmed - Mathematical Modeling of HER2 Signaling Pathway: Implications for Breast Cancer Therapy**

The cancer stem cell hypothesis states that there is a small subset of tumor cells, called cancer stem cells (CSCs), that are responsible for the proliferation and resistance to therapy of tumors. CSCs have the ability to self-renew and differentiate to form the nontumorigenic cells found in tumors. Over-expression of human epidermal growth factor receptor 2 (HER2) plays a role in regulation of CSC population in breast cancer. Current cancer therapy includes drugs that block HER2, however, patients can develop anti-HER2 drug resistance. Downstream of HER2 is nuclear factor κB (NFκB). The aberrant regulation of NFκB leads to cancer growth, which makes it a promising target for cancer therapy, especially for those who have developed resistance to anti-HER2 treatment. Our collaborator's lab has discovered that interleukin-1 (IL1), which is downstream of HER2, is responsible for NFκB activation, thus making it a potential target for cancer treatment. We have developed a mathematical model to represent the dynamics of this signaling pathway. Simulations of the model match experimental results, confirming the new pathway. We will use the mathematical model to make predictions for different scenarios, and it will be updated and expanded based upon new experiments.

**Sameed Ahmed - SIAM Student Chapter: Why You Should Participate!**

We will describe the USC SIAM Student Chapter. We will mention some benefits of joining SIAM and being an active member of the USC SIAM Student Chapter.

**Candace Bethea - The Grothendieck Group: What is it and Where to Find it**

The Grothendieck group construction of a monoid is a universal construction in algebra that appears in many different places in algebraic geometry. Intuitively, the Grothendieck group of a monoid is the abelian group that is "closest" to the original monoid. We will discuss this construction, how it applies to algebraic objects besides monoids, and uses for the Grothendieck group in different areas of mathematics.

**Joe Foster - An Introduction to Minimal Surfaces**

A Minimal Surface is a surface whose mean curvature is 0. The study of such surfaces goes back to Lagrange in 1762 who was tying to find surfaces of least area, stretched along a closed contour. In this talk we will see many examples of such surfaces (i.e. lots of colourful pictures) and one viewpoint as to how they may be studied, namely by their Enneper-Weierstrass Representation. This representation allows one to calculate information about such surfaces very easily and also construct new surfaces via transformations.

**Julie Lang - The Spring Number of a Graph**

A subset of vertices C of a graph G is a dominating set if each vertex of G is either in G or is adjacent to a vertex in C. The cardinality of a minimum dominating set is the domination number. A dominating set C is an identifying code if N[v] ∩ C is distinct for all v ∈ V(G), and the cardinality of a minimum identifying code is the identification number. The identification number is bounded below by the domination number. We will examine graphs with equal domination and identification numbers. In doing so, we will define the spring number of a graph.

**Jeremiah Southwick - Residue Completeness of Generalized Fibonacci Sequences mod m**

A generalized Fibonacci sequence is a sequence satisfying the Fibonacci relation. We call such a sequence complete mod m if all residues appear when the sequence is considered mod m. We will study this definition and will conclude by determining both necessary and sufficient conditions on the modulus m for a sequence to be complete mod m. Along the way we will highlight the importance of the Fibonacci numbers and the Lucas numbers, and will consider an invariant of generalized Fibonacci sequences that plays a key role in the results.

For more information about this seminar and previous semesters' line-ups, see last semester's seminar page.