### Citations

88 |
Tannakian categories. In: Hodge cycles, motives, and Shimura varieties
- Deligne, Milne
- 1981
(Show Context)
Citation Context ...ts identity connected component. Under the comparison isomorphism V ⊗Q Ql ∼= Vl, the Mumford-Tate conjecture predicts that: Conjecture 3. For any prime l, we have the equality G◦l/Ql = MT(A)×Q Ql. In =-=[3]-=-, Deligne proved the following: Theorem 2. For any prime l, we have the inclusion G◦l/Ql ⊆ MT(A)×Q Ql. My work is concerned with the case that A/F is an absolutely simple abelian fourfolds with trivia... |

86 | Congestion control for high performance, stability, and fairness in general networks
- Paganini, Wang, et al.
- 2005
(Show Context)
Citation Context ...itions on control parameters, e.g., feedback gains, for the closed-loop system to be stable. I intend to characterize these conditions, applying ideas from the research on Internet congestion control =-=[12]-=- and coupled oscillators [13]. The current modus operandi of power systems relies on generator-side mechanisms including automatic voltage regulation (AVR), power system stabilizer (PSS), droop contro... |

63 |
A note on Shimura’s paper “Discontinuous groups and abelian varieties
- Mumford
- 1969
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Citation Context ...d by Noot [16] that the second case happens to the Lie algebra of MT(A)/Q together with its action on V if and only if A/F comes from an analytic family of abelian varieties constructed by Mumford in =-=[10]-=-. Noot also proved in [15] that if the Lie algebra of G◦l/Ql together with its action on Vl is of the second case for one prime l, it is true for all primes l’s, and we call A/F an abelian variety wit... |

62 | Classical and overconvergent modular forms
- Coleman
- 1996
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Citation Context ...e result also has some interesting consequences. Let N be an integer prime to p. For each integer k we use M†k(Γ1(N)) to denote the space of overconvergent p-adic modular forms of level N over Cp. In =-=[2]-=-, Coleman constructed a linear map θk−1 : M†2−k(Γ1(N)) → M†k(Γ1(N)) such that the effect of θk−1 on the q-expansions is given by the differential operator (q ddq ) k−1. He proved that for k ≥ 2, every... |

50 |
Linearity properties of Shimura varieties
- Moonen
- 1998
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Citation Context ...erre-Tate coordinates on the deformation space ([5]). Moreover, the Serre-Tate deformation theory can be applied to determine the local structure of Shimura varieties of Hodge type at ordinary locus (=-=[11]-=-,[14]). My research has been forcused on applying the Serre-Tate theory to two types of questions in arithmetic geometry: the first is the study of the local behavior of Galois representations attache... |

33 |
adic algebraic monodromy groups, cocharacters, and the Mumford-Tate conjecture
- Pink
- 1998
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Citation Context ... 3 Bin Zhao Research Statement We now start with an abelian variety A/F with Galois representation of Mumford’s type (so we make no assumption on the existence of the Shimura curve C as above). Pink (=-=[17]-=-) proved that there is a subset Ω of finite places of F with Dirichlet density 1 at which A/F has good ordinary reduction. In [20], combining previous results developed by Noot ([16]) with Theorem 3, ... |

31 |
Serre-Tate local moduli, Algebraic surfaces (Orsay
- Katz
- 1976
(Show Context)
Citation Context ...riety A is ordinary, there is a structure of formal group on the infinitesimal deformation space of A/k, and any deformation of A is determined by the Serre-Tate coordinates on the deformation space (=-=[5]-=-). Moreover, the Serre-Tate deformation theory can be applied to determine the local structure of Shimura varieties of Hodge type at ordinary locus ([11],[14]). My research has been forcused on applyi... |

23 | Design and stability of loadside primary frequency control in power systems
- Zhao, Topcu, et al.
- 2014
(Show Context)
Citation Context ...oad scope of convex cost functions, we designed completely decentralized primary frequency control where every participant only measures its local frequency, and no explicit communication is required =-=[2]-=-. By further manipulating the underlying optimization, we designed distributed secondary frequency control, where every participant only measures its local frequency and power flows and communicates w... |

21 | Synchronization in oscillator networks: switching topologies and non-homogeneous delays
- Papachristodoulou, Jadbabaie
(Show Context)
Citation Context ... e.g., feedback gains, for the closed-loop system to be stable. I intend to characterize these conditions, applying ideas from the research on Internet congestion control [12] and coupled oscillators =-=[13]-=-. The current modus operandi of power systems relies on generator-side mechanisms including automatic voltage regulation (AVR), power system stabilizer (PSS), droop control, and AGC. Any novel control... |

19 | Connecting automatic generation control and economic dispatch from an optimization view
- Li, Chen, et al.
(Show Context)
Citation Context ...arch My paper [2] has been cited more than 50 times since May 2014. The idea in this paper has been applied by other researchers in improving economic efficiency of automatic generation control (AGC) =-=[9]-=-, reverse-forward engineering of power systems [10], and so on. An important application of distributed frequency control is load-side participation. In simulations of IEEE systems on Power System Too... |

17 | Anticyclotomic Main Conjectures
- Hida
(Show Context)
Citation Context ... ( 1 ∗ 0 2 ) , where 1, 2 are two characters of Dp. When f is a binary theta series of the norm form of a CM quadratic extension M of F (we say that f has complex multiplication in this case, see =-=[7]-=- section 6.2 for the construction), then the local representation ρf,λ|Dp splits. When F = Q, R.Greenberg asked whether the local representation ρf,λ|Dp splits only when f has complex multiplication. ... |

15 | Models of Shimura varieties in mixed characteristc
- Noot
- 1996
(Show Context)
Citation Context ...Tate coordinates on the deformation space ([5]). Moreover, the Serre-Tate deformation theory can be applied to determine the local structure of Shimura varieties of Hodge type at ordinary locus ([11],=-=[14]-=-). My research has been forcused on applying the Serre-Tate theory to two types of questions in arithmetic geometry: the first is the study of the local behavior of Galois representations attached to ... |

14 |
Abelian varieties—Galois representation and properties of ordinary reduction
- Noot
- 1995
(Show Context)
Citation Context ...analytic family of abelian fourfolds was generalized to that of abelian varieties of dimension 4k for all k ≥ 1. The properties of ordinary reduction of these abelian varieties have been discussed in =-=[13]-=-, which establish step (a). The rest three steps are generalization of the argument in [15] and [20] with appropriate modification. Hence the method in [20] can be applied to these abelian varieties w... |

11 | Local indecomposability of Tate modules of non CM abelian varieties with real multiplication
- Hida
(Show Context)
Citation Context ..., then the local Galois representation ρf,λ|Dp does not split. The proof is based on Hida’s result on the local indecomposability of Tate modules of non CM abelian varieties with real multiplication (=-=[8]-=-). It gives a positive answer to Greenberg’s question for all weight 2 elliptic modular eigenforms. Also it implies results in [1] under the assumption (H). The above result also has some interesting ... |

10 |
Abelian varieties with l-adic Galois representation of Mumford’s type
- Noot
(Show Context)
Citation Context ...cond case happens to the Lie algebra of MT(A)/Q together with its action on V if and only if A/F comes from an analytic family of abelian varieties constructed by Mumford in [10]. Noot also proved in =-=[15]-=- that if the Lie algebra of G◦l/Ql together with its action on Vl is of the second case for one prime l, it is true for all primes l’s, and we call A/F an abelian variety with Galois representation of... |

8 | On the local behaviour of ordinary Λ-adic representations
- Ghate, Vatsal
- 2005
(Show Context)
Citation Context ...n F = Q, R.Greenberg asked whether the local representation ρf,λ|Dp splits only when f has complex multiplication. This question has been studied by B.Balasubramanyam, E.Ghate and V.Vatsal in [1] and =-=[4]-=-. To state my result, I need to impose the following assumption: (H) if the degree [F : Q] is even, there exists some finite place v of F such that piv is square integrable, where pif = ⊗wpiw is the a... |

8 | Local indecomposability of Hilbert modular Galois representations
- Zhao
(Show Context)
Citation Context ... local behavior of Galois representations attached to nearly ordinary Hilbert modular forms; the second is the study of special cases of the Mumford-Tate conjecture. I will give a summary of my work (=-=[19]-=-,[20]) toward these two directions below. 1 Local behavior of Hilbert modular Galois representations Let F be a totally real field inside an algebraic closure Q̄ of Q and let FA be the adele ring of F... |

8 | Swing dynamics as primaldual algorithm for optimal load control
- Zhao, Topcu, et al.
- 2012
(Show Context)
Citation Context ...ment. My research addresses this issue by establishing a novel design and analysis framework for distributed frequency control, in two directions. Direction 1: Optimization-based controller design In =-=[1]-=- we proved that the swing dynamics of synchronous generators, the linearized power flows, and the droop control can together be identified as a real-time primal-dual algorithm to solve an optimization... |

6 |
Hodge classes and Tate classes on simple abelian fourfolds
- Moonen, Zarhin
- 1995
(Show Context)
Citation Context ... My work is concerned with the case that A/F is an absolutely simple abelian fourfolds with trivial endomorphism algebra, i.e. End◦(A/F̄ ) = Q. In this case, from the calculation of Moonen and Zarhin =-=[12]-=-, there are two possibilities for the Lie algebra of MT(A)/Q together with its action on V (resp. the Lie algebra of G◦l/Ql together with its action on Vl) when base changed to an algebraic closure of... |

6 | Reverse and forward engineering of frequency control in power networks
- You, Chen
- 2014
(Show Context)
Citation Context ...s since May 2014. The idea in this paper has been applied by other researchers in improving economic efficiency of automatic generation control (AGC) [9], reverse-forward engineering of power systems =-=[10]-=-, and so on. An important application of distributed frequency control is load-side participation. In simulations of IEEE systems on Power System Toolbox, we showed that the load-side distributed freq... |

6 | Frequency-based load control in power systems
- Zhao, Topcu, et al.
(Show Context)
Citation Context ...led at low rates or without a global clock. This motivates the study of robustness of endpoint-based control to low time-resolution or asynchronous measurements, on which we have a preliminary result =-=[11]-=-. Moreover, the measurements may not be available at every network bus, in which case an investigation of system observability and detectability is necessary. Furthermore, I would like to design endpo... |

5 |
On Mumford’s families of abelian varieties
- Noot
(Show Context)
Citation Context ...r c of the Lie algebra; 2. c⊕ sl2⊕ sl2⊕ sl2, with the 1-dimensional center c, and the representation of sl2⊕ sl2⊕ sl2 is the tensor product of the standard representation of sl2. It is proved by Noot =-=[16]-=- that the second case happens to the Lie algebra of MT(A)/Q together with its action on V if and only if A/F comes from an analytic family of abelian varieties constructed by Mumford in [10]. Noot als... |

5 | Fast load control with stochastic frequency measurement
- Zhao, Topcu, et al.
- 2012
(Show Context)
Citation Context ...r all the participants, thus minimizing the total cost of control. In addition, distributed communication is able to mitigate the negative effect of measurement noise, as shown in our earlier studies =-=[7]-=-, [8]. Intuitively, a tradeoff must be made between communication cost and controller performance. Impact of my research My paper [2] has been cited more than 50 times since May 2014. The idea in this... |

4 |
On algebraic cycles on surfaces and Abelian varieties. Izv. Akad. Nauk SSSR
- Tankeev
- 1981
(Show Context)
Citation Context ...the previous step to construct the MumfordTate group of A/F . As is clear from the proof in [20], there is much room for a generalization of our argument to abelian varieties of higher dimensions. In =-=[18]-=-, Mumford’s construction of analytic family of abelian fourfolds was generalized to that of abelian varieties of dimension 4k for all k ≥ 1. The properties of ordinary reduction of these abelian varie... |

2 |
On local Galois representations associated to ordinary Hilbert modular forms
- Balasubramanyam, Ghate, et al.
(Show Context)
Citation Context ...its. When F = Q, R.Greenberg asked whether the local representation ρf,λ|Dp splits only when f has complex multiplication. This question has been studied by B.Balasubramanyam, E.Ghate and V.Vatsal in =-=[1]-=- and [4]. To state my result, I need to impose the following assumption: (H) if the degree [F : Q] is even, there exists some finite place v of F such that piv is square integrable, where pif = ⊗wpiw ... |

2 | Optimal decentralized primary frequency control in power networks
- Zhao, Low
- 2014
(Show Context)
Citation Context ...zation-based framework in Direction 1 no longer provides a straightforward stability proof, since the underlying optimization is nonconvex and therefore its primal-dual algorithm may not converge. In =-=[4]-=-, [5], we performed compositional stability analysis for the distributed primary and secondary frequency control designed with this framework. We proved asymptotic stability of the closed-loop system ... |

2 |
load control via frequency measurement and neighborhood area communication
- “Optimal
- 2013
(Show Context)
Citation Context ... the participants, thus minimizing the total cost of control. In addition, distributed communication is able to mitigate the negative effect of measurement noise, as shown in our earlier studies [7], =-=[8]-=-. Intuitively, a tradeoff must be made between communication cost and controller performance. Impact of my research My paper [2] has been cited more than 50 times since May 2014. The idea in this pape... |

1 |
Λ-adic p-divisible groups I,II. lecture notes at
- Hida
- 2005
(Show Context)
Citation Context ... variation of local Galois representations on a Hida family as to prove the previous results. This question has intimate relationship with the properties of Λ-adic Barsotti-Tate groups constructed in =-=[6]-=- and [9], which is another subject I am interested in; 2. the second project is to establish new cases of Mumford-Tate conjecture. For an abelian variety A/F as in Theorem 4, the argument in [20] cons... |

1 |
Λ-adic p-divisible groups
- Hida
(Show Context)
Citation Context ...on of local Galois representations on a Hida family as to prove the previous results. This question has intimate relationship with the properties of Λ-adic Barsotti-Tate groups constructed in [6] and =-=[9]-=-, which is another subject I am interested in; 2. the second project is to establish new cases of Mumford-Tate conjecture. For an abelian variety A/F as in Theorem 4, the argument in [20] consists of ... |

1 | On the Mumford-Tate conjecture of abelian fourfolds, preprint available at http://www.math.ucla.edu/ zhaobin/MTAV4.pdf
- Zhao
(Show Context)
Citation Context ...l behavior of Galois representations attached to nearly ordinary Hilbert modular forms; the second is the study of special cases of the Mumford-Tate conjecture. I will give a summary of my work ([19],=-=[20]-=-) toward these two directions below. 1 Local behavior of Hilbert modular Galois representations Let F be a totally real field inside an algebraic closure Q̄ of Q and let FA be the adele ring of F . Fi... |

1 | A unified framework for frequency control and congestion management in low-inertia power systems
- Zhao, Enrique, et al.
(Show Context)
Citation Context ...inal values, but also enforces thermal limits of transmission lines such that the N − 1 security criterion and chance constraints in economic dispatch can be relaxed, resulting in significant savings =-=[3]-=-. Direction 2: Stabilizing nonlinear dynamics A linearized model is adequate for frequency control today, but in the future, a more accurate nonlinear model must be used to deal with high volatility o... |

1 | Distributed generator and load-side secondary frequency control in power networks
- Zhao, Mallada, et al.
- 2015
(Show Context)
Citation Context ...n-based framework in Direction 1 no longer provides a straightforward stability proof, since the underlying optimization is nonconvex and therefore its primal-dual algorithm may not converge. In [4], =-=[5]-=-, we performed compositional stability analysis for the distributed primary and secondary frequency control designed with this framework. We proved asymptotic stability of the closed-loop system by ch... |

1 | Distributed frequency control for stability and economic dispatch in power networks
- Zhao, Mallada, et al.
- 2015
(Show Context)
Citation Context ...or different power network models, controllers, actuators, and communication schemes. My research along this line provides valuable insight into the role of communication in controlling a network. In =-=[6]-=- we proved that completely decentralized frequency integral control without any explicit communication globally stabilizes a network with nonlinear power flows to an equilibrium with nominal frequency... |

1 | Optimal sizing of voltage control devices for distribution circuit with intermittent load
- Zhao, Chertkov, et al.
- 2015
(Show Context)
Citation Context ...trol, considering the speed of response, ramp rate, capacity, and operating cost of each resource. The performance improvement from such allocation is observed in my previous work on Volt/Var control =-=[14]-=-. The third task, motivated by a recent study [15], is to design market mechanisms which implement economic dispatch while providing appropriate incentives for endpoint-based control. Concluding remar... |

1 |
Distributed optimization decomposition for joint economic dispatch and frequency regulation
- Cai, Mallada, et al.
- 2015
(Show Context)
Citation Context ..., capacity, and operating cost of each resource. The performance improvement from such allocation is observed in my previous work on Volt/Var control [14]. The third task, motivated by a recent study =-=[15]-=-, is to design market mechanisms which implement economic dispatch while providing appropriate incentives for endpoint-based control. Concluding remarks The power grid is rapidly evolving, so is its c... |