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Life sciences

I have been working to model leukemias in humans using mathematics. Leukemias are cancers of the hematopoietic system. Most of the mathematical models I have formulated so far, have been ODE models. We would like to understand things like expansion of leukemic cells in different stages of cell cycles. Molecular targeted therapy (imatinib mesylate) is available for chronic myeloid leukemia (CML). I am interested in learning whether we can optimize drug therapy at the patient level. We can try to minimize the amount of drug, or the time taken for the therapy or a host of other factors. Since CML develops resistance to targeted therapy, we would also like to understand the relapse mechanism. My collaborators are medical doctors like Dr. Cecil Ross a hemato-oncologist at St. John's Hospital , and scientists like Sudhir Krishna at NCBS.
Some of my math collaborators in developing these models are Suzanne Lenhart , Helen Moore , L.G. de Pillis , and Ami Radunskaya .

Projects in mathematical biology, undertaken with students:

2008 (summer)
Prabhat Kumar (IIT Kharagpur). He did a study of math models of Glucose- Insulin Dynamics with the purpose of modeling diabetes. He wrote many programs to model these dynamics based on existing work in the literature and conducted several numerical experiments.

2010 (summer)
Shubham Dipt (IISER Kolkata) and Balaji Prasanna (NIT, Bhopal)- summer 2010. They deconstructed the model proposed by Michor et al (2006) and suggested improvements.
Arpit Dua (IIT, Roorkee). (Joint student with Sudhir Krishna, NCBS). He worked on modeling the effects of aneuploidy on tumor growth.

Finance

I worked for a few years for a Wall Street firm that no longer exists. This is where I got interested in problems in mathematical finance. The following students have done various projects with me:

2007
Ravi Thanvi, IIT Kharagpur (summer).
Tirupam Goel, IIT Kanpur (summer). Tirupam now works at HSBC.

2008
Swapnil Kumar, IIT Delhi (summer)
Abhinav Srivastava, IIT, Kharagpur (summer)
Ratna Sinroja, Bombay University, (Academic year 2008-2009). Ratna now works for BRICS Securities in Mumbai.

2009
Swapnil Kumar, IIT Delhi (summer). Swapnil now works at a trading desk in Gurgaon.

MTECH students: Swapnil Kumar and Chandan Shikha Dua did their Master's thesis entitled Stochastic Volatility Models in Option Pricing with Srikanth Iyer and me. Chandan now works at an IT firm in Chandigarh.

Industry Projects

Helicopter Rotor Balancing, Merlinhawk Associates, 2006-2007. Collaborators: Mythily Ramaswamy (TIFR-CAM) and Anindya Chatterjee (IIT, Kharagpur). Project assistant Sarath Sasi (now at Mississipi State University).
Understanding Volatility, Kotak Securities, 2007-2008. Collaborators: Srikanth Iyer(IISc), Swapnil Kumar, Abhinav Srivastava.

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