# Workshop on the Global Attractor Conjecture

## Details:

Date: March 11-13, 2016

Location: San Jose State University

## Registration:

Attendance at the March workshop will be free of charge but capped at 25 people. Please apply by completing this form.

## Agenda:

The Global Attractor Conjecture (GAC) is one of the oldest and best studied problems within Chemical Reaction Network Theory (CRNT). Since its formulation in the early 1970s, the conjecture has resulted in a flurry of research activity, dozens of papers, and a litany of false proofs. (The result is so intuitive, in fact, that the authors of the canonical 1972 paper "General Mass Action Kinetics" errantly believed they had already proved the result when they first stated it!)

In his recent manuscript "Toric Differential Inclusions and a Proof of the Global Attractor Conjecture", Professor Gheorge Craciun (UW Madison) proposes a proof of the conjecture. The manuscript represents the culmination of nearly a decade of work, and involves complex ideas from dynamical systems, differential inclusions, and algebraic geometry. It is the intention of the workshop to go through the manuscript in detail, and see if this giant of CRNT has truly been slain.

## Schedule:

Breaks in **MH 331B**

Talks in **MH 322**

#### Friday, March 11:

1:30-2:15 p.m.: Registration/Reception (MacQuarrie Hall 331B)

2:15-2:30 p.m.: Welcome from Organizers

2:30-3:30 p.m.: Introductory Talk (Gheorghe Craciun)

3:30-4:00 p.m.: Break/Coffee

4:00-4:45 p.m.: Perspective Talk (Frank Sottile)

4:45-5:00 p.m.: Break

5:00-5:30 p.m.: South Bay Reading Group Update (Nikki Meshkat or Matthew Johnston)

5:30-6:00 p.m.: East Bay Reading Group Update (David Dynerman or Bernd Sturmfels)

#### Saturday, March 12:

9:00-9:30 a.m.: Reception/Coffee

9:30-10:30 a.m.: Discussion (Section 3)

10:30-10:45 a.m.: Break

10:45-11:30 a.m.: Discussion (Section 4.1 and 4.2)

11:30-11:45 a.m.: Break

11:45-12:30 p.m.: Discussion (Section 4.3)

12:30-2:00 p.m.: Lunch

2:00-2:40 p.m.: Discussion (Section 4.3, cont.)

2:45-3:25 p.m.: Discussion (Section 4.3, cont.)

3:30-4:10 p.m.: Discussion (Section 4.3, cont.)

4:10-4:30 p.m.: Break

4:30-5:30 p.m.: Discussion (open)

7:30 p.m.: Group dinner at Farmer's Union

#### Sunday, March 13:

8:30-9:00 a.m.: Reception/Coffee

9:00-10:15 a.m.: Discussion (Section 4.4)

10:15-10:30 a.m.: Break

10:30-11:30 a.m.: Discussion (Section 4.5 and Section 5)

11:30-1:00 p.m.: Lunch

1:00-1:45 p.m.: Discussion and new directions

1:45-2:00 p.m.: Break

2:00-3:00 p.m.: Open Problems (participants are welcome to present open problems during
this period, sign up on spreadsheet)

3:00-3:30 p.m.: Closing Remarks

Sign-up spreadsheet

## Related Events:

The workshop will be preceded by a number of seminars in the Bay Area, split between UC Berkeley and San Jose State University. Attendance is strongly encouraged!

**November 23 (5:00-6:00pm), UC Berkeley (891 Evans):**Introduction to Toric Dynamical Systems, Bernd Sturmfels**January 15 (10:00am-3:00pm), UC Berkeley (939 Evans):**Seminar on Mathematics of Biochemical Reaction Systems (Part I) (Agenda)**January 18 (11:00am-4:00pm), UC Berkeley (939 Evans):**Seminar on Mathematics of Biochemical Reaction Systems (Part II) (Agenda)**February 8 (5:00-6:00pm), UC Berkeley (939 Evans):**

Global Attractor Conjecture Reading Group (Meeting I)**February 16 (3:00-4:00pm), San Jose State University (MH320):**

An Introduction to the Global Attractor Conjecture**February 22 (5:00-6:00pm), UC Berkeley (939 Evans):**

Global Attractor Conjecture Reading Group (Meeting II)**February 23 (3:00-4:00pm), San Jose State University (MH320):**

Reading Seminar (Meeting II)**March 1 (3:00-4:00pm), San Jose State University (MH320):**Reading Seminar (Meeting III)

## Organizers:

Matthew D. Johnston (San Jose State University)

Elizabeth Gross (San Jose State University)

Nikki Meshkat (Santa Clara University)

Bernd Sturmfels (UC Berkeley)

## Participants (tentative):

Shabeena Ahmed (West Valley College)

Eric Au (SJSU)

James Brunner (UW-Madison)

Lynn Chua (UC Berkeley)

Gheorghe Craciun (UW-Madison)

David Dynerman (UC Berkeley)

Chris Eur (UC Berkeley)

Gilles Gnacadja (Amgen)

Martin Helmer (UC Berkeley)

Serkan Hosten (SFSU)

Badal Joshi (CSUSM)

Nida Obatake (SJSU)

Casian Pantea (WVU)

Anna Seigal (UC Berkeley)

Anne Shiu (Texas A&M)

Frank Sottile (Texas A&M)

Janos Toth (Budapest Univ. Tech. Econ.)

## Accommodations:

*Mention SJSU when booking!*

The Westin San Jose 302 S. Market St. San Jose, CA 95113 408-295-2000 |
Hotel De Anza 233 W. Santa Clara St San Jose, CA 95113 408-286-1000 |

Hyatt Place 282 S. Almaden Blvd San Jose, CA 95113 408-998-0400 |
Four Points by Sheraton San Jose Downtown 211 S 1st St San Jose, CA 95113 408-282-8800 |

Economy options are also available on the VTA light rail line close to the airport.
The VTA is $2/ride and drops off at 1st Street and San Antonio (3 blocks from SJSU
campus).

Caravelle Inn & Suites |
San Jose Airport Inn |

Motel 6 San Jose Airport |
EZ 8 Motel San Jose II |

## References on the GAC:

- F. J. M. Horn and R. Jackson, "General Mass Action Kinetics",
*Archive Rational Mech.*,**47**:81-116, 1972 - F. Horn, "Necessary and sufficient conditions for complex balancing in chemical kinetics",
*Arch. Ration. Mech. Anal.*,**49**:172-186, 1972. - M. Feinberg, "Complex balancing in general kinetic systems",
*Arch. Rational Mech. Anal.*,**49**:187-194, 1972 - M. Feinberg, Lectures on Chemical Reaction Networks, written version of lectures given at the Mathematical Research Center, University of Wisconsin, Madison WI, 1979. Available at http://www.crnt.osu.edu/LecturesOnReactionNetworks
- P. Érdi and J. Tóth, "Mathematical models of chemical reactions",
*Manchester University Press*, 1989. - D. Siegel and Y. F. Chen, "Global stability of deficiency zero chemical networks",
*Can. Appl. Math. Q.*,**2**(3):413-434, 1994 - D. Siegel and D. MacLean, "Global stability of complex balanced mechanisms",
*J. Math. Chem.*,**27**(1-2):89-110, 2000 - D. Angeli, P. Leenheer, and E. Sontag, "A petri net approach to the study of persistence
in chemical reaction networks",
*Math. Biosci.*,**210**(2):598-618, 2007. - G. Craciun, A. Dickenstein, A. Shiu, and B. Sturmfels, "Toric dynamical systems",
*J. Symbolic Comput.*,**44**(11):1551-1565, 2009 - D. Anderson and A. Shiu, "The dynamics of weakly reversible population processes near
facets",
*SIAM J. Appl. Math.*,**70**(6):1840-1858, 2010 - D. Siegel and M. D. Johnston, "A stratum approach to global stability of complex balanced
systems",
*Dyn. Syst.*,**26**(2):125-146, 2011 - M. D. Johnston and D. Siegel, "Weak dynamic non-emptiability and persistence of chemical
kinetics systems",
*SIAM J. Appl. Math.*,**71**(4):1263-1279, 2011 - D. Anderson, "A proof of the global attractor conjecture in the single linkage class
case",
*SIAM J. Appl. Math.*,**71**(4):1487-1508, 2011 - D. Angeli, P. de Leenheer, and E.D. Sontag, "Persistence results for chemical reaction
networks with time-dependent kinetics and no global conservation laws",
*SIAM J. Appl. Math.,***71**:128-146, 2011 - Casian Pantea, "On the persistence and global stability of mass-action systems",
*SIAM J. Math. Anal.*,**44**(3), 2012 - G. Craciun, C. Pantea, and F. Nazarov, "Persistence and permanence of mass-action
and power-law dynamical systems",
*SIAM J. Appl. Math.*,**73**(1):305-329, 2013 - P. Donnell and M. Banaji, "Local and global stability of equilibria for a class of
chemical reaction networks",
*SIAM J. Appl. Dyn. Syst.,***12**(2):899-920, 2013 - M. Gopalkrishnan, E. Miller, and A. Shiu, "A projection argument for differential
inclusions, with applications to persistence of mass-action kinetics",
*SIGMA,***9**:25, 2013 - M. Gopalkrishnan, E. Miller, and A. Shiu, "A geometric approach to the global attractor
conjecture",
*SIAM J. Appl. Dyn. Syst.*,**13**(2):758-797, 2014