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|| || uh-oh, I am stuck, and I think I need a cofee or beer to get through
Differential equations (PDEs, ODEs and FDEs), difference equations,
applied dynamical systems, mathematical biology.
Why these ?
- Things are changing in the real world, and differential
equations are equations involing derivatives which are rates of
changes. This is why differential equations are so important in
understanding many changing phenomenons in nature, including those in
biology, physics, and
even economics and finance. And this is also why I am interested in DEs
and their applications.
- It is commonly agreed that much of the mathematics in the 20th century
was driven by physiscs. Now it is also widely believed that much of
the mathematics in this century will be driven by biology---there are so
many biological questions that can not be answered merely by
biologists. It is high time for applied mathematicians to get in.
Among my works on applications of DEs to biological problems are the following
featured examples of problem driven nature:
- Why so many un-mutated bacteria can survive antibiotics? Oh, it is due to the altruistic role of the mutated
- There are many species of virus in the real world, but why some choose budding while the others choose lytic way to release from their host cells
in their replications?
Read this for an explanation.
- A variety of maralia species are currently endemic in different regions around the world, but is it possible for two different species to be co-peristent in a single region?
- Asian long horn beetle invaded Canada in middle 2000's, causing panic in the West of GTA. Would the cut-burn control strategy work to eradicate this invasive beetle?
Read Analytically Solving the Beetle Problem, which received A Nugget from SIAM , and was selected to republish, as a SIGEST paper, in SIAM Reviews (SIAM Rev. 53(2011), 321-345).
- Coming with the seasonal flu is a new flu for which there is no vaccine yet,
would taking the seasonal flu vaccine be of any use/help in preventing the new flu?
Well, it depends
Funding (I am grateful to all
these programs/agents from which I have received funding):
- NSERC Discovery (2016-2021): $40,000 x 5
- MITAC Elite PDF funding (2012-2013): $35,000
- Ontario Ministry of Natural Resources (2011-2014): $55,000
- NSERC Discovery Accelerator Supplements (2010-2013): $40,000 x3
- NSERC Discovery (2010-2016): $35,000 x 6
- Ontario Ministry of Science, Technology and Industry (PREA, 2005-2010):$140,000
- NSERC Discovery (2005-2010): $20,000 x 5
- Fields Institute (with L. Wahl and G. Webb, 2005):$10,000
- NSF (USA) (with L. Wahl and G. Webb, 2005): $7000
- MITAC-NCE (2005--2008, 2008---2012): $91,000
- University of Western Ontario (Start-up, 2004-2006): $15,000
- AARMS, Fields Institute and CRM (with H. Brunner and X.-Q. Zhao, 2004): $26,000
- Petro-Canada Young Innovator Award(2002-2004): $25,000
- NSERC Discovery (2000-2005): $15,000x 5
- MITAC-NCE Fund (with S. Campbell et al, 1999-2002): $194,000
- CFI (with D. Pike et al, 1999): $75,000
- Memorial University of Newfoundland (Start-up, 1999-2002):$25,000